In Manila I would stay at the Cherry Blossom Hotel by Robinsons place in Ermita - close to Roxas Avenue -nice free breakfast - close by is the Lotus Garden Hotel - a bit more money but a nice breakfast buffet.
In Cebu the Diplomat Hotel is nice for the money - a nice lower price place just off Mango Avenue is the on Jakosalem is the Alto Pension house
Tune hotels are consistently ok - clean with good beds - can be booked at a good price on Agoda
None of these places will have that long list of pool weight room etc - i dont think u can find that place for around 25 bucks in the Philippines
I dont know anything about Bangkok
I just got back from Bangkok . I've been going there almost every year for the last 20 years.
You'll have difficulty easily finding a cheap hotel meeting your pool and weight room specs - especially in the tourist areas. There's another way to do this though. I don't know how long you're going to be in Bangkok, but you might want to think about going on Craigs list and looking at rooms for rent.
There's a lot of interesting stuff there, including condos and larger homes with pools and gyms. Some of them appear to be really cheap. Like around 12,000 baht (about $363) a month.
Be forewarned though. Thailand, especially the touristed part, is not what it was 20 years ago. If I was you I'd be looking to get out of the tourist areas of Bangkok, and preferably out of Bangkok itself as soon as possible. Head for the hills where the people are still nice.
I often stay at no star hotels, but in the best room, then buy a membership to the 5 star hotels for 30 bucks. I did a video on Lake Atitlan about the Porto Lago Hotel showing the pool, and weight room. Note, I could care less about the Star system, I see it as just a marketing ploy.