Osaka is the bigger financial hub and city, but for tourists the attractions are just the Castle (looks more impressive outside than inside and if you see Himeji Castle then it's skippable), Dotonburi (the nightlife street), the Aquarium, and the Universal theme park - the latter 2 may or may not be of interest. You can cover in a day unless you want to go to Universal, and if you're also visiting Tokyo the Dotonburi is a nice experience but not groundbreaking.

Nara is well-worth a visit but you can easily do the deer park and shrines in a day (more likely half-day b/c you'll get shrined out).

Kyoto, on the other hand, is worth a minimum of 2 but should be ~3-4 days (can stretch even more if you want to go at a slow pace / relax). Due to WW2 you won't find the historic center and quality of shrines of Kyoto in many other Japanese cities, so you'll be spending far more time here. It's far more relevant for sightseers hence there are way more luxury properties here than in Osaka (which is debatable if it has a property that meets this forums guidelines).

So if you decide to spend ~5 days in the region, basing yourself in Osaka would mean ~2+ hours of train commutes 4 out of the 5 days which sounds tedious. If budget is a concern I would just look at more reasonably priced properties (up-scale but not relevant to this forum) in Kyoto - there are lots of decent but not luxury chains or even ryokans in Kyoto.