Typical conference hotel, good for business, good for leisure
This Hyatt is, well, a Hyatt. You expect excellent accommodations, food, and service and you'll get them. Check-in was super-fast without all the 3rd degree you get at other hotels (needing to show all sorts of ID, filling out forms, etc.). The lobby was mostly uncrowded and quiet even at different times of the day. You can sit and read, work, or relax inside or outside on the comfortable furniture.
I was there for a 5-day business meeting/conference and most everything went smoothly. There was another conference meeting in and around our scheduled rooms which caused some confusion but no problems. The food prepared and served by the hotel staff in the conference rooms and ballrooms was surprisingly good and still warm when served. We had breakfast, lunch, and dinner on several occasions and nothing to complain about.
The rooms were large and had the usual amenities. The skin, toilet, and tub was in the same room. Towels were thick and fluffy and even the toilet tissue was softer than most other hotels (if you pay attention to that sort of thing). The TV had about 40 channels but I couldn't get the radio to get more than a few stations that were either country music or Spanish language. The window overlooked the interior of the hotel (atrium) rather than outdoors - I'm not sure if there are any rooms with outside views.
The fitness center was crowded, even at 6 AM! There were about a dozen cardio machines and all but one was occupied. Free weights and machines were available. I swam once in the outside pool which is on the top floor (roof, actually) and you can see the skyline and get a nice birdseye view of downtown San Antonio. 
The Alamo is one block away and the ground floor of the hotel opens up to the Riverwalk. So it's easy to get to where you want to go if you're a tourist.
We spent time at Q, which is the lobby bar, and the food and beverages were quite good. Tacos and baked potatoes and other bar food was a cut above and not terribly expensive (for example, I paid $5 for a loaded baked potato and the bartender threw in a Diet Pepsi free).
Did anything go wrong? Yes. No hotel is perfect. :) The major problem was that the wireless Internet service, supposedly free in the lobby, kept starting and stopping randomly throughout the day and night. I've never seen so many disconnected-connected signals on my iPad. I gave up after a while and used my hot spot card. This continued all 5 days I was there and other people had trouble as well. I've never quite figured out why budget hotels offer free Internet that works well and expensive hotels charge extra for poor-quality wireless. Oh, well.
I recommend the Hyatt for either business or for hanging out in downtown San Antonio. There are many large and small hotels in the immediate area, so lots of choices. I don't think you can go wrong at the Hyatt or the other major chains.