You can find Western-style hotels in all big cities, including all major chains, with a large choice of places. Rooms are usually small and sometimes even divided in two sides to optimize the space if you just want to occupy two beds, but in general they are modern and full of little amenities like pijamas, slippers and toothbrushes. Most hotels have free wifi and both continental or Japanese breakfasts and normally they would have somebody who can speak English.
Other Western-style accommodation are hostels and guesthouses, that are much more abundant in Japan than you may think - some of them really looking more like modern hotels than the crappy places you have in mind! We stayed in a couple that really surprised us in terms of organization, cleanness and services, so I really recommend them, especially if you are only in that place for one night and you need an easy and convenient place to stay. The girls particularly enjoyed the atmosphere in some of them, and loved to hang out in the communal areas where you usually meet all kinds of travelers.
There are other very Japanese ways of spending the night, like capsules hotels or love hotels that we haven't tried any of those.