If you're new to traveling to Asia you can be surprised by the number of tiny businesses and street shops and that sort of venue are obviously cash based businesses (if the shop doesn't have an actual cash register, take the hint). But for the serious kind of boutiques, restaurants, hotels and the like, credit cards are fine. When I visited Japan I was still using mostly my MasterCard and it was never turned down in places I'd expect them to take a CC.
Still, overall, I'd say Japan is quite more cash based than North America, but it's not that bad either. It's nowhere near like, say Thailand, where you may as well just leave your CC in the hotel safe. There's ATMs everywhere anyway, so after a day you will have a good feel how much you need to carry and you will adjust just fine. It really depend what kind of spender you are and where you hang out, so there's no set rule. Worst case scenario an employee will walk you to the nearest ATM to get cash to pay your bill.