Hmmm. I guess this depends on how old your son is [edit in: sorry, I missed that he was 14], and more about your own tolerance, or enjoyment of change is. Me? I like to settle down in a place. It is only after 3 days or more that I feel ok. When I know where I'm eating, the way to the gym, etc. Then maybe at 7-10 days do I really feel like I'm in something. It also depends on how heavily or often you want to train. Every day? Twice a day? Or taking days off?
Just giving you my own sense, I'd say two weeks minimum for a single gym experience, once you know you like it, which means once you start moving again the next stay will feel shortened. When we first came to Thailand we committed in advance to two experiences over I think 6 weeks. I really loved our stay in Chiang Mai at Lanna at the time. Then, perfectly happy, we went down to Bangkok and Sasiprapa. The Bangkok experience wasn't bad in anyway, but we actually wished we had just stayed in Chiang Mai. It was far less gritty, the gym experience was really nice. It wasn't the worst thing to push for two, but it wasn't ideal.
I would maybe make a first choice of location, and then a list of 3 gyms in that location. I'd go to each of them for a day and just feel what it is like and go by intuition. Can I picture myself here for 2 weeks? If you find a great one, one you really vibe on, then just stop there, no need to push for more. I'd give myself 10 days in that first choice gym. After about 7 of those days I'd reassessed. Do I want to change gyms? Or do I want to change cities? If you are really happy where you are, just stay. It's pretty easy, and not that expensive to just hop on a plane and be somewhere else if you suddenly get the urge to have a different experience. Don't pay for lots of days in advance, especially in the time of COVID when tourism is going to be down. Everyone will be glad to have you. Keep things flexible.