As Paul11 says, cash (including ATMs) are the way to go in Japan. You may have trouble getting a credit card accepted, especially MasterCard, and don't even think about cash advances with your credit card.
For accommodation, check
www.metropolis.jp for Tokyo and Osaka Time Out for Osaka. Many ads are geared to budget travelers.
For the onsen, you will be able to join your boyfriend in the rotenburo (open air bath) in many places in Nagano and Gunma, and just about anywhere if you go up to Tohoku. Most onsen inns (ryokan) also have private baths, just try the door, if it's unlocked it's yours.
I personally recommend Kanazawa. The geisha quarter is a smaller version of Gion in Kyoto, and though it is touristed the other tourists will be 99% Japanese. Himeji and Okayama Castles are of great historical interest.
Go to Akihabara in Tokyo and hang out in a maid cafe!