Talk to your travel agent first. This is the best way to help yourself find the list of hotels you would like to stay in. Japan is a big place and has so many spots to visit, which means there are so many hotels that you will be confused to decide which ones can fit your budget.
Finding hotels without the help of a travel agent will take a lot of time and energy, but surely you do not want to spend hours looking for cheap hotels on the Internet. Talk to your travel agent about different options of accommodation. Travel agents usually know about accommodation in big cities, and they will be able to give you a list after reviewing your budget.
Visit the website of Japan National Tourism Organization and try to get as much information about hotels as you can. The website of Japan National Tourism Organization is a one stop shop for all your tourism needs. You can a long list of hotels on the website.
If the accommodation charges are an issue for you, you can select a number of hotels and check with them through their website one by one. Visiting the official pages of each hotel will help you decide which one of them will fit your budget.
Search for hotels on the Internet. If you have no time to rush to your travel agent or dash off an email asking for a list of hotels, you can give the Internet search a try.
Use Google search to find out about some of the most affordable hotels in the cities you plan to visit. Google search can give you plenty of sources to help you find what you are after. Note down every single detail and compare the prices of different hotels and their packages.