I'm staying in Shinsaibashi because it's central but trying to get out and do atypical things. I went to Kobe and it was nice. And the beef was delicious.
Osaka is the city I'm the most familiar with in the Kansai area so I can give you some recommendations based on that.
・Umeda is as previously mentioned more tourist free and is the central part of northern Osaka. There are a number of big department stores in the area such as Hankyuu, Hanshin, Daimaru and Lucua. Each department store has at least one restaurant floor at the top and oftentimes one at the bottom too. Additionally, Hankyuu, Hanshin and IIRC Daimaru all have a food product floor where you can buy bentos, confectionary and other stuff.
It's easy to get lost but in my opinion it's easily one of the best areas of Osaka.
・Tennouji is a good area for a long walk as you'll find lots of random temples/shrines. For lunch/dinner you can go to the shopping center Mio Plaza (it's connected directly to the station) as there's a restaurant floor there.
・The Tsuruhashi area is known for the local Koreatown. There's an old market located right next to the station that's like an underground labyrinth and where you can find a lot of food stalls and tiny stores. Overall the number of tourists is very low, except Koreatown typically has some Korean tourists, and this is another area where you can just take long walks.
Some Japanese people are suspicious of the area because of the high proportion of Korean residents, but I never felt unsafe there (and overall "unsafe" in Japan is nothing compared to the worst neighborhoods of North America and Europe) and in recent decades even a lot of Japanese non-residents have been making their way there since the yakiniku is cheaper and there's a wider selection of meat available compared to most other places.
・If you like train rides I recommend taking the Chuuou line from Honmachi to Cosmosquare and then getting on the New Tram line at the same station. That way you'll get a great view of the Osaka harbor and some of the neighborhoods of southern Osaka. From the final stop Suminoe Kouen you can then take the Yottsubashi line to get back to Honmachi or go to Nanba.
Important: if you decide to go to Honmachi again you'll need to briefly exit at one of the stations before that and then enter the metro again, because it's not possible to get out at the same station where you entered. Otherwise you'll need to ask one of the station guards to let you out.
Edit: if you'd want to make more than a brief stop I recommend either getting off at Kujou on the Chuuou line (there's a shoutengai close to the station) or at Suminoe kouen (the park there is nice for a walk).
・The Minoh park is located in the northern part of the prefecture and is well-known for its big waterfall and the Katsuoji temple. In the autumn it's pretty crowded but there shouldn't be too many people there right now. Instead of taking the Midousuji line and then the bus I recommend taking the Hankyuu Takarazuka line from Umeda and then getting off at Ishibashi Handai-mae to take the Minoh line to Minoh station.