I did a homestay for a month in Fukuoka recently, and I wanted to share my experience in case anyone is wondering about it, since it was very positive!
I applied with this company: Best to learn Japanese | Homestay in Japan
I contacted them a few months in advance and had to do advanced payment for the whole stay, and I received the details of my host family about a month before the trip. Just a note that I did not have a choice in the matter, but from the description I got a thought it was a good match. Clearly homestays are mostly used by students and I am 40, but they still found a family for me. I also did not go to a language school but to a regular aikido training. The family was really nice and caring to me, we usually had breakfast and dinner together, and they made an effort to ask me questions and prompt conversation in Japanese. They also included me in their family New Years celebration and invited me to their activities if I wanted to join. I think we found a balance between me participating but also not invading their family life too much.
Also a note that homestay is much cheaper as compared to a stay in any hotel. The commute time to my training destination was about 40-50 min (the agency offers to find a family with a commute up to 1h). The language and cultural exposure is invaluable, I would recommend it to anyone studying Japanese.