If you want an AI most likely you will be out of town or down in Playacar, which means that a taxi will cost more than $5.
If you want a beachfront hotel in town, it won't be AI, and you won't really have a lot of "activities" provided, unless you seek them out yourself. But you will be close enough to walk everywhere or take a taxi for about $2.
What about Grand Coco Bay? It doesn't always get the best reviews, but it's an AI in the north section of town that allows kids, and I think it's pretty affordable. Whenever I used to walk by it, I always thought it looked nice.