Serviced Apartments and Share Houses
For short stays in Tokyo, and indeed for the rest of Japan, hotels are very convenient. However, you should be aware that hotels in Japan typically charge per head, and not per room (there are exceptions), so hotels can become an expensive proposition.
The alternative to hotels, are serviced or furnished accommodations, or share houses. There are many levels of serviced or furnished accomodations in Tokyo, so it really depends on your budget, but options are available from around 160,000 per month up into the the millions of yen per month.
Serviced accommodations provide services such as concierges and maid services, where as furnished accomodations often don't have these options.
If you are looking for cheaper options, there are now many share houses around Tokyo for much less monthly costs. You can acquire a room for well under 100,000 yen per month, and then just need to be prepared to share washing facilities, bathrooms, kitchens, etc.
For very short stays of less than 1 month or less than a couple of weeks, please be aware that hotels may be your only option. In order to operate short-stay operations in Japan you need to have a hotel license and meet certain hotel standards. Short stays are therefore not possible for many serviced and furnished options, as their stays are limited to one month or more (the upside being those facilities don't need to meet hotel standards, so monthly fees are likely to be more cost effective than hotels or serviced accommodations that have a hotel level of service.