Personally the most expensive part of a Japan trip is really the airfare for us. It was more than $4k for two of us RT the past October. However, the hotels are extremely inexpensive by our standards. I know one we stayed at was $60 (Tokyo Asakusa). Outside of the Hilton we stayed at for Disney I believe the most expensive hotel was mid-$300 for the ryokan (traditional Japanese inn) the rest being $100-$200 per night. Food is very inexpensive and many things like temples and whatnot are inexpensive or free. Trains are not that expensive overall either. Tickets for Tokyo Disney aren't expensive either although unfortunately there isn't a whole lot that can be done to save costs on hotels if you're staying right there (we stayed at Hilton Tokyo Bay). A tip would be to also consider a weekday pass or a weekend pass for Disney. This allows you entry into the parks at 5pm for the weekday and 3pm for the weekend; although it's curtailing your park hours it can save on costs. We did a weekday pass for the evening we arrived back in Tokyo from Takayama thereby still getting in some park time at a reduced price of what a full day would have been and using the evening time more strategically (instead of just doing nothing).
If I have a suggestion it would be go expand beyond Tokyo especially because you have that time there. Fly to Japan but only going there you're missing so much for all that effort plus talk about costs Tokyo may be costing you more than other areas out there.
We actually only spent a night in Tokyo and looped back for just Disney (one evening at DL, full day at DL, two days at Disney Sea) but outside of that we saw Kamakura, Hakone (where the ryokan was, also went to the volcano/sulphur there), Kyoto, Nara, Kanazawa and Takayama and that's just basically touring central Japan. We sacrificed Tokyo to see other places and sacrificed other places to do Disney but we got to see a lot more of their culture by expanding outside of Tokyo; I'd also add a lot of tourists go to just Tokyo, Kyoto and Osaka missing other places.