Coffee (コーヒー kōhī) is very readily available in Japan in a variety of forms and quality. Yes, you can find a large variety of super cheap canned coffee in vending machines and convenience stores; however I'd rather describe those as caffeinated soft drinks with coffee-ish flavor than as coffee.
Instant and filter coffee ("drip" coffee, ドリップ) is very easy to get almost anywhere; supermarkets and convenience stores sell one-cup coffee-in-filter sets you just need to add hot water to, some convenience stores sell fresh hot coffee either from a pot or a machine, "family restaurants" like Denny's or Gusto (ガスト) offer full western style breakfasts (somewhat japanized of course) where the coffee usually comes from a machine. Most restaurants will have a standard selection of coffee on their menu, except Japanese speciality places (like sushi or udon restaurants). If this is good enough for you, you'll be able to get by just fine.
Starbucks and a whole bunch of competing chains (Doutor, Tully's, Beck's, Veloce, Excelsior) are all over the place, typically at least one of them near every train station or at the local department store, except for very out-of-the-way places. You should be able to get a decent shot of coffee there in every major and mid-sized city. You can usually get your coffee hotto (hot) or aisu (cold).
Aside from those there are many independent cafés (カフェ kafe) every here and there. Some very old-fashioned places specialize in romanticized western coffee tradition (dim light, counter seats and booths) and usually carry some form of 珈琲館 kōhīkan in the name. Others are more places to socialize which incidentally sell coffee; take your pick. A lot of these places carry the same selection of coffee, Key Coffee and UCC are big brands and often part of the signage.
You may or may not get a coffee at your ryokan; unless they're extremely old fashioned they'll probably have something, but whether that suits your taste or not you won't know until you try. Modern hotels usually have something to offer. At the very least you'll be able to make a filter or instant coffee with hot water in your room.
Should you insist on a very specific sort of beans brewed just so, you may have a bit of a hard time. But as long as standard "international" coffee (black, latte/au lait, cappuccino, espresso) is fine for you, Japan has enough of it. Whatever coffee you will get will probably be pretty good for what it is; can coffee doesn't compare to a fresh shot under any circumstances, but can be very nice with the right expectations. Standard restaurant machine coffee will be decent for what it is. Starbucks & co. are fine for what they are. You'll be hard pressed to find a truly terrible coffee in any category.