There are several reasonably good gay travel websites with some of the information you want. I'll post a few more below.
As for price, Japan is considerably less expensive now than Singapore. The Japanese ¥ has fallen in value by over 35% since pre-covid even though they now have as many, if not more, visitors than pre-covid. Today the rate stands at USD1=¥151. 5 years ago it was ¥110. 13 years ago it was ¥75.
With this being sakura season, hotel prices are artificially high for a couple of weeks. Looking at agoda, in June there are plenty of 3-star hotels in the popular Shinjuku area for between USD85 and 120. Drop a star and the price drops. But note that prices in Japan are dependent to a large extent on room area. The lower the price, the smaller the area.
Food is not expensive if you eat at the many local noodle, curry and other restaurants. Certainly a meal can cost under USD10. Also there are inexpensive convenience stores like Family Mart and 7 11 just about every corner with the usual sandwiches, noodles and a host of other items you can take back to your hotel. But if you are after more gourmet fare, the sky can be the limit unless you go for lunch when set menus tend to be a fraction of what you'd pay in the evening.
Here's a typical host bar site (sorry don't know how to get actual pics up)
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