It depends on when and where you stay. Of course, the festive season is more expensive, but not that much more expensive. You can get a reasonably priced hotel on Jan 2nd; I did and it was a nice hotel!
If you are staying in Tokyo, then 10,000 JPY per night per room (2 people) seems right. The outskirts of Tokyo, e.g. Yokohama, is a bit cheaper but not too much. If you are in the other large cities such as Nagoya, Kyoto and Fukuoka, expect the price to be about 70% of that.
Osaka seems to be the cheapest so far, and I can often get extremely cheap hotel rooms in Osaka (actually, in Umeda, one of the two central business areas, making it even more surprising), but don't count on it. It's just my experience, although I go to Osaka often.
The prices in central Tokyo can also vary a lot by area, as well. According to my experience, Akihabara, Nihombashi, Shimbashi and Akasaka (surprising because it's a rather upscale neighborhood) tend to be cheap, while the commercial areas such as Shinjuku, Shibuya, as well as Odaiba, tend to be expensive. Your mileage may vary.
As for the local cities, it is almost never necessary to stay away from the city center for low prices. In fact, in smaller major cities like Sendai, there are no hotels outside of the city center anyways.
The above prices will get you a so-called "business" hotel, with all amenities (including microwave and mini-fridge!) but nothing fancy. Usually, there's a desk and a bed, and that's it. The room tends to be small.
One step up from the business hotel is the city hotel, which is more like the standard hotel room in another country. Think Hilton or Sheraton. The rooms are spacious, with chairs and sofas, etc., and better furniture. Usually, it will be about 1.5~2 times the price of a business hotel, but often there are good deals allowing you to stay in those hotels at a cheap price. If the city hotels are priced similarly to a business hotel, I would usually be willing to pay 1000-2000 JPY extra for a city hotel.
So, business hotels (and/or cheap city hotels) seems suitable for your budget.
If you want to go lower than that, you can try (of course) Airbnb, hostels, or minshuku (already mentioned in other answers). Or even a capsule hotel, which is dirt cheap but quite uncomfortable. Note that capsule hotels are designed for solo travellers/backpackers, and a hotel room for 2 is often not much more expensive than 2 capsules.
You can even sleep in a net cafe or karaoke box, but that's for when you are super desperate.
If you stay at a hot spring resort, you will probably want to stay in a ryokan. These can be quite expensive (Tokyo city hotel price ranges), but they often include authentic Japanese-style full service dining and free access to the hot springs. Plus, it is the uniquely Japanese experience that every visitor should try out :-)
There are also more modern hot spring resorts that function more like a hotel, but also serve traditional Japanese dining (although often more like a restaurant), and often also with traditional Japanese-style rooms. They tend to be cheaper and more modern than the ryokan, so you might or might not like it better.
Finally, let me mention the love hotel. A love hotel is basically a "motel" in some countries, primarily used for, uh, intimate needs. However, one can also stay in them. Often, they are actually quite nice to stay, and their price do not fluctuate much with regards to date. So when hotels are expensive, the love hotels can be a very good deal. However, love hotels tend to reject (1) solo guests, (2) male couples or groups of men (groups of women are usually accepted), and of course (3) larger groups. If you are travelling with a partner, then the love hotel is something to try!