If you wish a park with all kinds of amenities there is the Admiralty RV Park on the west side of the 1604 loop. It is quite a distance from downtown and not a fun drive but you will be close to Sea World and an amusement park which I think is Six Flags. Blazing Star is also out there but it has a steep drive coming in and out and the sites were far from level. We stayed there once and will not be seen there again.
If you wish to be close to downtown there is Traveler's World. It is not a fancy park but quiet and the people were friendly. It is about 3 miles from the Alamo and you can drive there easily by car or take the city bus that stops across the street. You will also be in the middle of the Mission district with, if my memory is correct, 4 more missions within a couple of miles of the park.