*Fallout 1 is generally well balanced for any Combat Boy build. Melee is a big part of early game, but the weapons unfortunately peter out until you find a top tier weapon like a Super Sledge or a Ripper. This is a general problem in the game for the most part, but the game is well build for a Combat Boy and Super Mutants aren't too tough. Fallout 1 is perfectly suited for a melee build. Master is tough to take on with just melee, but a few EMP Grenades should kill him just fine if you're not up for the challenge.
*Fallout 2 starts you out with a pretty alright melee weapon, however the difficulty curve is all over the place in this game and soon you will face a brick wall around the time of Vault City-Gecko chapter. You are simply too fragile to take on enemies with high tier weapons, in large numbers, at that point in the game, so you will definitely have to get a bit of help from companions or ranged weapons(in my case handguns and thrown items like grenades) to stand a chance as a pure Combat Boy character. Enclave are much tougher than Super Mutants and going up against them with a pure melee character isn't a good idea, same goes for taking on Frank Horrigan. Restoration Project added in an Easter Egg Lightsaber weapon, but it's post game content, to give melee characters a bit of an edge I added it to the EPA so Science Boys can get an Infinity Plus One Sword for their playthrus, same kind of reward they get in the form of Skynet(best sniper companion in the game) if they specialize in that skill.
*Fallout 3 has some interesting balance compared to other games, but one of the more interesting designs is that one of the best vanilla melee weapons is available really early(Shishkebab). Since the game is in 3D now, there is a bit more nuance, for example you have low AP weapons that deal less damage but can potentially be more useful for high-crit characters. Then, you have OP DLC weapons like The Auto Axe or Jingwei's ShockSword, this makes melee one of the most rewarding and nuanced builds in the game with many options available even early on. As Fallout 3 is infamously impossible to finish without at least a few combat encounters, and there is overall a lot more fighting than in other entries, you will be getting into scraps often. Samurai Armor from MotherShip Zeta additionally increases Melee Damage by a flat 10 no matter what, so if you're going all-in on this build, you can look cool while doing so, too. It is almost impossible to take down some enemies with melee, for example turrets or snipers, so it's best to have a secondary ranged weapon or grenades as well.
*New Vegas is the most well balanced entry in the franchise, and there is a ton of variety both early, mid as well as late game. Everyone has a taste or a preference, my favorites are the DLC weapons you can get like Blade of West or Proton Axe. Poisons are very interesting, but ultimately they are a meme, you won't even find enough throwing weapons outside of Honest Hearts of Dead Money if you want to go down that route and poisons for melee weapons are overkill unless you're trying to take down a Deathclaw with one for some reason. Overall, very enjoyable and perfectly doable, but then again so is every other Combat Boy build, no matter how niche.
Here are my observations for side games and mods. Note that these are heavily modded, so your mileage may vary if you try these yourselves:
*Fallout Tactics is infamously unbalanced to hell and back. There is dozens of redundant weapons that are useless by the time you find them and even if they were present in the first mission, they would still be nearly worthless. Other weapons have way too little niche ammo so you will never use them after you run dry, some builds are downright impossible end game since they do nearly no damage to end game foes. Melee is very shafted in this game(pun not intended), you get nearly no good weapons outside the tried classics like Ripper or Cattle Prod, both of which are available nearly immediately(second mission if you play your cards right, finding ammo for them is a bigger problem). Vast amount of new weapons means nothing if most of them are nearly identical to one another, you are never going to debate if you want to use an Axe Handle(blade missing) or a simple Raider Club, you will just use whatever you find laying around first, and frankly melee combat is nearly suicidal in this game as is, even if it was good. Even Deathclaw recruits are garbage since you get them far too late and they cannot wear any armor. That said, I had to mod in an end game tier variation of every good melee weapon just so that these builds could stand a chance and even then it is not viable. My melee character was mostly using grenades and handguns this run, so my advice? Don't run melee or unarmed builds, they are completely unviable in Tactics. These are fallback weapons, if you really want to experiment just pick a pre-made recruit from the yeoman who will likely do better in close range combat than you can. Stick to shotguns or SMGs for close encounters.
*New California is a short prequel mod, but it favors melee heavily. There is a ton of new melee weapons and there is a lot of end-game drops spawning in the short time you play this mod. This is good, since a good portion of it involves combat, especially the finale. This mod is perfectly suited for both Combat Boys and melee fighters, you even get to bring some toys into Mojave since after the mod is over, you just start the proper New Vegas campaign again with your gear stashed away(location depends on your ending) and any remaining companions found somewhere in the overworld as well.
*London is very melee focused, but like many entries, you will likely spec out into ranged weapons over time. Early game is brutal, you don't even get a guaranteed melee weapon until nearly the end of the tutorial in the form of a useless cane, and the guaranteed knife you get after is complete garbage too. Early game is unforgiving and you will find yourself using a ranged weapon on nearly anything that isn't the most weak enemy in the game, like a radroach. Once you get your strength back, then the build comes into it's own and you get a decent variety of weapons. Unfortunately, there is no downright OP weapons and the enemies continue to scale endlessly like in Fallout 4, so past a certain point you will not be able to do enough damage with just melee weapons. The game also suffers from the same problem as Tactics, in which there is way too many of them but most are derivative or downright garbage. I suggest modding in your favorite melee weapons from Nexus, most of them should easily be compatible and found within standardized spawning lists.
*Nevada is an interesting case since the game is much harder than most other entries, even Fallout 2. On the other hand, most encounters are fairly balanced, and you should have no problem with them if you're prepared, unlike Fallout 2 which can drop 20 armed opponents on you the moment you leave the tutorial zone and get you killed in a fight which you cannot win. End game melee weapons are interesting, as there is an extra tier of melee weapons compared to Fallout 1 and 2. Good luck finding some of them, I recommend a guide. Unfortunately, the end game is notoriously difficult for Combat Boys, and due to armor being hot garbage in this game(yes, even Power Armor) you will likely not be able to go in as a Combat Boy and have to either sneak or talk your way thru some of the end game, or at least use more powerful ranged options(Vault filled to the brim with one-hit-kill turrets is one such example, peek around corners and use EMP grenades). Early to mid game should be viable, however.
I haven't finished TTW yet, but the Capital Wasteland chapter so far is very interesting. Weapon meta is largely the same as in Fallout 3, however thanks to the NV mechanics the early and mid games are much harder. At the same time, you appreciate some of the overlooked aspects of the game, like poisons, in here than in Mojave. Of course, TTW doesn't add Capital Wasteland compatible poisons, so I had to mod many of my own. Melee weapons are largely the same as far as their meta goes, but due to their high damage, they are much more viable for end game and DLC high level threats over guns that might not even penetrate. That goes double for Enclave, whose Power Armor is a proper threat now vs cardboard armor in Fallout 3. Melee or Pulse Grenades are the best option to deal with them, so I recommend using both in this run. With how much junk there is in DC, playing a Mad Bomber in conjunction with melee is very rewarding, I also have robots(as I talked about earlier) that add even more strategy into the mix.
As for Fallout 4, from what I remember the meta there is that melee characters are very powerful, however weapons variety in the game are lacking. You will either hope for good Legendary weapons or go for end-game tier DLC weapons that will make the game trivial, such as the guaranteed Staggering Ripper in Far Harbor, the high DPS Bleeding Shiv in Nuka World or the radiation hammer in Far Harbor. Same problem as in London, where the mobs will eventually get too powerful, but with how powerful weapons are here versus there, you will have to play for quite a long time for that to become an issue. Unlike in London, you also get Power Armor without modding the game, and there is also powerful armor for non-PA builds like Grognak's Outfit, so there is definitely some variety. Lastly, grenades got a massive buff and you can finally hotkey them without needing a mod, so weapons like Frags and Molotovs got a massive boost and synergize with melee builds well. Interesting how Automatron works here vs RobCo Certified.