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Yes, for most people Japan does tend to be more expensive to travel. I don't know what your budget is, but if you're there for a couple weeks and traveling outside Tokyo, you probably want to get a JR (Japan Rail) pass. It's expensive, but definitely cheaper than buying individual tickets on the train. Otherwise, take the buses wherever you can, they are much cheaper but slower.
Food isn't too crazy if you look carefully, you can find lots of great ramen places, or go to the convenience stores. Plan a special meal at a nice sushi restaurant (or just stick to conveyor belt sushi), but otherwise budget your food costs to save money. You can do lots of cheap sightseeing, so save money there.
If you're not staying in a hostel or capsule hotel, the best thing is to use miles or points if you have them. If you spend time looking, you can hopefully find the best value for your points. Otherwise you could try couchsurfing. If you have to pay more for accommodations, you should probably skip the train pass and just do more bus travel and local exploring.
I think most people would budget at least $100-200 USD per day to travel in Japan. You could probably get by on $50/day if you're really good at budgeting (a minimum of 6,000 yen). It's going to be tough without staying in a hostel at all. Hopefully you can spend at least $100/day, that will give you more options.