Hi,
The only two things from your list that are location specific is the gym and dog park.
The only decent gym that I found is MVP in Spanish Springs. I live south of 466A, and it takes 20 minutes to drive there in a car. So too far.
There are 3 dog parks in The Villages. The one near me is 10 minutes by car and is crappy. There is one near Spanish Springs in Paradise Village. It's a little small, but the people are fabulous. There is a huge one up near Rt 42 at the most Northern part of The Villages. I haven't been to that one. And there is a private one, off of 466 near the rt 301 side of The Villages.
Sounds like neighborhoods near Spanish Springs will get you everything you need.
Good luck and you are gonna love it here!!!!!!