One could only hope parks of all types would be points of interest with their own place category. But it seems not.
All I can see so far is that you get some results with FindNearBy Method.
The returned object has a couple options.
1) as you mention search for "park" in the object.Location.Name
2) Check object.PlaceCategory.Index = 7 for campgrounds
3) Check object.PlaceCategory.Index = 14 for Landmarks and then try to determine if it is a "park" as in step 1.
If you find some better way let us know. I could use "park" information when reverse goecoding vehicle location. The boss always seems to be interested in the vans parked in a park.
ciao,