I spend a lot of time in Del Rio in the fall/winter because I hunt there, but I have never dived Amistad in the winter...too cold for me. I would assume that viz is much improved over the summer. In the summer, best viz is near the hydrilla beds and is maybe 20 feet. There is a scuba cove at Diablo East (part of the Nat'l Park) that is roped off from boat traffic. Access is through stairs from the parking lot, and there are picnic tables and restrooms there. Depth is about 40-50 feet depending on lake level. For most anything else, you will need to rent a boat. I am not aware of anyone running organized trips on the lake, but ask around. The National Parks Service has a visitor's center on Hw 90 before you get to the lake that can provide more info.
I have not been diving in Amistad a lot but can give you some first hand info from a frequent tourist.
The best hotel by far is the Hampton Inn. It is less than 2 years old, and clean. I think that you have to enter the main building to get to all the rooms, so carrying gear into your rooms is more of a hassle than direct access to the parking lot like Days Inn, etc. The Ramada is also ok, but you will not mistake any hotel in Del Rio for the Ritz-Carlton.
Restaurants are limited, unless you like fast food. I like Wright's Steakhouse and Cripple Creek Restautant. Both are Texas-style casual dining and are good (order chicken fried steak). They both are on Hw 90 between Amistad and town. Sirloin Stockade is buffet style akin to Golden Corral. Contrary to what you might think, I have not found a good Mexican restaurant this side of the border.
There are 2 dive shops in town that I know of. One is called Amistad Divers and it is located in the same building as the propane dealership on Veteran's Blvd west of town. It has a limited selection of gear, and I am sure they can fill tanks. There is also another place that is new that flies a dive flag out front (also on Veteran's Blvd) but I have not been in there and don't know the name. Best bet is to call one of them for further info on diving. Check the Chamber of Commerce web site, also.
For other activities, you can always go to Acuna, Mexico if you are into that border-town kind of thing. You can get into as much trouble as you want over there. The winery is also a good way to spend some time. Also, Seminole Canyon state park is west of Del Rio and has some desert hiking with nice views of the Rio Grande and old indian cave paintings.
Overall, Del Rio/Amistad is a nice place to spend some time, and they have some of the biggest bass in the state if you like to fish.