Sleep on Tokyo

Hotels.

Budget

One hotel that does not have a curfew is Kangaroo Hotel, rooms starting at ¥3200 = $33,35. There's also Economy Hotel Hoteiya, rooms starting at ¥2500 = $26,06.

One of the cheapest ways to stay can be also a youth hostel, prices start at ¥1200 = 12,51.

If you are truly on a budget, it is possible to go homeless and camp in public parks, for free. You can do this with a tent, if you want to carry one.

Mid-range

Keep an eye out for what is called a business hotel. The rooms are usually tiny, but they are easily located near stations and tax start from around ¥6000 = $62,64.

If you plan to stay more than one week, you can try Weekly-Mansion Tokyo. Rates are around ¥5000 = $52,13 per day for one person or a little more for two people.

In a city as expensive as Tokyo "cheap" is definitely a relative term. Japanese hotels in general and Tokyo hotels particularly, can be a bit expensive. In Tokyo a luxury hotel can easily cost $1,000 = ¥95940 per night, and even mid-range hotels cost anywhere from $250-$350 = ¥23985 - ¥33579 per night.