A walk from Montgomery, Alabama to Auburn, Alabama is 21 hours.
When I was living in the college town (not Auburn nor Tuscaloosa), I could walk around the campus and to the gas station/Waffle House. Walking to the store? hell no.
Wow this is really tough, you can navigate within both cities decently well, but the margins are razor thin on practically every road in and out, or the interstate, which you should avoid. The country roads seem decentl flat and low traffic, you might do well on those.
Route 110 is not an interstate and it is legal to walk it, and has a pretty good margin on one side, I'd choose that. But the whole way it's going to be a struggle in that transition between highly developed city and open rural. Like the intersection between 110 and 231.
I'd say your best case scenario is:
Basically being on full alertness, very slow pace here I'd expect as your negotiate with vehicle traffic, as all of these have razor thin margins, you should expect to walk in the grass for a lot of this, this will likely take 2 days, not 1:
108, 110, try your damnedest to survive the intersection with I-85.
126, relax a bit when you get to the more comfortable but still expecting more grass and gravel. 80, 40.
Very low traffic at this point, you can probably expect to have multiple minutes between passing cars.
9, 17 which appear to have well walked footpaths to the side.
Back to more grass and gravel with 49, 56, 37, 54.
You'll arrive in the small town of Notasulga probably late at night, assuming you started early in the morning. Buy what you need at the gas station then curl up on the doorstep on one of the churches and cry yourself to sleep.
In the morning, follow 14 to Auburn, more grass and gravel, higher traffic that slowly increases, You are blessed with a decently maintained railroad that closely follows the road, and is not fenced off, you can carefully navigate the side of it. The surface is pretty dull with no fresh metal at all in the street view, so it's probably hardly used, but you should still be careful with it especially in morning and evening.
You can expect to arrive in Auburn in the late afternoon.
Sidewalks and crosswalks everywhere again, so easy going from here. Head on over to Grub Mart for what I'd expect to be 5 star food, head over to the rec center and pay for a membership so you can use their pool shower, then go to college so you can edumacate yourself on how to use greyhound.
Not a fun trip at all, could do with a walking path parallel to the highway, but I bet hardly anyone would use it because everyone drives anyways. People who don't drive find everything they need in their city limits and don't ever have to leave, and in fact, shouldn't.