Does your study abroad include dorm lodging/housing or do you need to book your own? If they provide housing, e-mail and ask if there are any options for arriving before or after your program and any associated fees. You could probably save a good bit on food if they allow access to their cafeteria. Some universities allow public access to their cafeterias and it'd allow you to get familiar with the food and ordering when you're on your own schedule.

Definitely compare hotel prices in English and Japanese (easiest way is to flip the tripadvisor locality to Japanese and use Google translate) if you want to compare the costs of arriving early/leaving late. Some of the English related booking engines also charge more in fees and taxes, in addition to showing higher rates. I've also found that mid-end non-Western hotel chains usually cost less than the Western brand. I'd probably disregard points/status and brand recognition if focusing on price.

Are you and your partner attending the study abroad together? Sharing a double room in a business hotel will probably be more economical than a capsule hotel for two people, especially if you get one with access to a washer, microwave, or included breakfast. A business hotel breakfast is the easiest meal to eat more vegetables and fruit if you are eating out on the cheap. Non-gift fruit is still more expensive than many Americans expect (unless you travel to farming communities). Restaurant ramen is cheaper than you'd probably expect from West Coast pricing.

You can also put the JR passes on your credit card if you plan on traveling outside of Tokyo. If you'll just be in Tokyo, pick up a Suica or Passmo with cash or in a bundle at the airport if they accept credit cards. They should code as travel for 3X UR. Suica/Passmo reloads are typically done with cash so no points there.