pitsheel, I spent an evening in Ponce while I was in Puerto Rico and while I didn't visit the Hilton, I wouldn't have wanted to stay more than a few hours in Ponce. We drove through some really unsavory neighborhoods to get to the main square - once we got there though, I will admit the square is adorable and has an incredible ice cream shop which is dirt cheap.
Most "outdoor activities" require a car. I would think a taxi would be very expensive to go anywhere further than old San Juan. In old San Juan I'd recommend visiting El Morro fort - there are always tons of families there hanging out in the park, flying kites, picnicing, etc. If you can find Palomas Park, it might be fun to take your kid there to see an unbelievable amount of pigeons (to be honest I found it a bit creepy but the kids there loved it!)
If you do rent a car, a visit to El Junque (the rainforest) is unforgettable. Amazing hikes through enormous "jurassic park"-like plant life, great interpretive center. You could probably get there on a tour bus out of the hotel, also. We did it by car though, so we were able to stop in Luquillo on the way back for the only cheap meal we ate the entire trip. There are lots of fun cheap shacks along the beach selling mostly fried fish but there are a few vegetarian options - mostly in the fried cheese category. Great pina coladas too.
The caves (forget their name) are also a neat tour that kids would enjoy. Definitely need a car or tour bus for that.
As for vegetarian options at the hotel ... we decided not to take advantage of the lounge, and ate breakfast at the Olas spa every day. They are expensive but have tons of vegetarian options for breakfast and lunch. Some days we got wraps (ie hummus and veggie) and vegetarian paella and other things to go, and took them with us.
In Old San Juan the Parrot Club had a fantastic roasted veggie and cheese sandwich on the lunch menu - also a "tower of vegetables" dinner plate that was very good. Fun atmosphere that both kids and adults would enjoy - but also on the expensive side.
We also had lunch one day in a cute hotel in Condado called Hosteria Del Mar that was fantastic for vegetarians. Condado has a great beach but I doubt you can use it unless you are staying there. We had a fantastic vegetarian lunch on a porch overlooking the beach (again, kind of pricey - $50 for 2 adults) - goat cheese appetizer with fried plantains to dip in it, home made veggie soup, some sort of wonderful green salad thing, interesting curry chayote entrée with all sorts of veggies and tofu in it.
Hope this helps!
- Truly