Osaka is a sleeper. I had the same impression as you before I visited it. Plenty of bad wraps on the web about Osaka. If you can get Hyatt on award, give Osaka a try. It is very easy and convenient to do day trip to Kyoto, Nara, Himeji and even north/west Japan (the J Alps). Hotels in Osaka are much less expensive than Kyoto & Nagoya.
I stayed in Nagoya Marriott Associa twice. Great hotel. Recall posted 1 report about it in Marriott forum long time ago.
http://www.flyertalk.com/forum/marri...cia-hotel.html

This year, Associa has dropped from Cat 5 to Cat 4. So if you have any Cat 1-4 eCerts, this is the best plac to use them. At 32,000 jpn a night, I’ll use eCerts first, and then points. If use points, buy 4 nights to get 5. (that’s how I stayed both times with 5 nights each). On my upcoming trip in the summer, I’ll use eCerts.
From Nagoya, I did day trips everywhere. To name a few, Toyota factory / museum, Himeji, Kobe, Osaka, Kyoto, Nara, Takayama. Nagoya itself has more sights than I expected. 2 full days is my guess. Many great places to eat.
The key to it all, get a JR pass.