I can't figure out why you think that going to Kyoto would cause you to spend more on accommodations.

Both Tokyo and Kyoto have accommodations in every price range, and unlike many other countries, you go pretty far into the budget hotel range without sacrificing cleanliness or safety.

If you REALLY want to stay in one hotel the whole time, for whatever reason, but want to see some Japanese cultural sites, go to Kamakura (home of the Great Buddha and other temples and shrines and close enough that people commute to Tokyo for work) or Nikko (a scenic area that features the family temple of the Tokugawa Shoguns).

Or, as people have suggested on another thread, fly into NRT and out of KIX, so that you don't have to make the two-way train journey.