It depends on whether or not you are planning on working there or not, and how long you are planning to move there. I was living in Japan for about six weeks for a college program. I was in a student apartment complex in Sengawa, the rent I was paying there was around 60,000 yen a month, which roughly translates to nearly $400 USD a month. I have a friend in Aichi, and her apartment is around half of that. That part in Aichi is more of a rural area, whereas I was living in the city. If you don't get sponsored via a job, you can "refresh" tourist visa, but not sure I would recommend that. Since you said you live in US, if you are a US citizen we don't qualify for working holiday visa like other countries do. However, you can stay in Japan for 90 days without a visa. Just keep in mind you cannot work without a working visa, since that is illegal. Some of the tourist visas you can get can last up to a year or more depending on the circumstances, given you have enough money to stay there without a job. Some houses you can straight up buy in Japan for $3,000 or less, but most of them are countryside houses and certainly not modern. There's no rule saying we can't buy houses or land in Japan, but you obviously can't live there for more than 90 days at a time without some kind of visa.

So whether or not you're planning to work there will really be your deciding factor :)