1) Get a Japan Rail Pass, like a Eurailpass for Japan. Second class is just fine and so much cheaper than single tickets that Japanese people nearly weep with envy when they hear about it. Like a Eurailpass, it must be purchased here.
2) Stay away from big Western-style hotels and concentrate on so-called business hotels, which almost are small and furnished like a college dorm but invariably clean and safe with a private bath. Expect to pay about $100 or less for a double. One of the most economical nationwide chains is the Toyoko Inn at
http://www.toyoko-inn.com, but there are others as well.
3) For more traditional accommodations, try a minshuku, or Japanese-style bed and breakfast (only with dinner included). These are mostly in smaller towns and cities.
4) Some business hotels supply a buffet breakfast, but otherwise, you can get a light breakfast called "morning service" or "morning set" in most coffee shops. These usually include coffee or black tea, toast or rolls, a hard-boiled egg, and maybe a tossed salad with vinaigrette dressing. For other meals, just walk around looking at the plastic or photographic displays of the menu items. If the prices are not listed, you can't afford it. If you need a mid-day caffeine fix, get it from a vending machine, a fast food joint, or a Dotour coffee bar and save a couple of dollars.
5) If you to do a lot of subway riding or travel on the private rail lines (neither of which is covered by the Japan Rail pass), get the local debit card (Passnet in Tokyo, Surutto Kansai in Kyoto-Osaka). There's no cost saving, but it's very convenient and doesn't expire.