I found that avoiding Western chains was - for the most part - key to getting a good yet inexpensive place to stay in Japan, when I visited there at the end of February/Beginning of March last year. I also found that you don't need anything more than a 3* hotel in order to get great accommodations. There are lots of Japanese hotel chains, including Dormy Inns, which are excellent.
Take Kyoto for example - While the Ritz and Hyatt in Kyoto were going for around $800 USD/night, I found an absolutely amazing 3* place called Hotel Anteroom (very highly rated on TripAdvisor) for less than $50 USD/night, and it absolutely blew me away. Granted it was not the Ritz, it was for a single room, didn't have so many amenities, and perhaps the location was *slightly* out of the way (but still walkable from the train station) it somewhat resembled (and was definitely as good as) a W Hotel. This place could easily pass for 4* if it had more amenities. I suppose one could stay at the Ritz or Hyatt if they've got money (or points) to burn, but really, you don't have to.
On the other hand, in Tokyo, I found an AMAZING Choice property (Comfort Hotel Tokyo Kanda) for about $85 USD/night, and that was for a twin room, single occupancy (recommended if you can get it!). Basic but very clean, and very quiet. The free breakfast was also much better than what you'd find in North American Comfort Inns too.
Now...for Narita, if you're a single traveller that needs a relatively basic place to crash near Narita and don't have status that will get you a free breakfast, take a look at the Narita View Hotel. Often, for around $50 USD (not including breakfast) one can get a single room there. I didn't try it, but apparently their breakfast is expensive yet extensive - though it might still be best to grab something at 7-11 at Narita for breakfast before you go if you don't eat much. It's definitely not the most modern hotel, but it was clean enough, and I got a free upgrade from a single room to a twin room without even asking! I didn't get a renovated room, but it was absolutely fine for 1 night. The hot spring (Onsen) was a very nice touch (even if you had to pay to get in).
Another notable hotel was the Beppu Station Hotel in Beppu, where I decided to take a side trip to because I couldn't get a hotel room in Kagoshima that night due to a marathon, and the place I'd purchased my JR Pass from suggested it when I mentioned I wanted to visit a hot spring town while I was in Japan. OK, now this place was a bit old (more so than the Narita View), the single room was 85 square feet (yep, you read that right!), and there was no such thing as a non-smoking room (at least the windows opened wide), but at $37 USD (no breakfast included - but it was available for an extra cost) on a Saturday night it was an incredible value compared to everything else - and most places seemed to be full. Yes...it was clean, AND it had an Onsen for guest use (again, old, but FREE!). I just needed a place to crash, and it more than served its purpose. I also liked that it was pretty well right next to the train station - as the name suggests.
In terms of the bathroom amenities, most hotels in the US don't have toothbrushes in the bathrooms. However, there was one at every single hotel I visited. On the other hand, you typically don't get small bottles of shampoo et al - these are in refillable bottles. In the $37 place in Beppu, they even had really good Shiseido bath products. Couldn't believe it!
In closing, do your research on TripAdvisor and Booking.com (as well as double checking with the hotel's website, if they have one)
You might find some great places to stay in Japan that won't cost you an arm and a leg.