For a tourist...
Food:
Taquitos West Avenue - good atmosphere, food is really good for a popular spot, and something a bit different than most of the rest of the US.
Pearl District- I like Southerleigh the best of the restaurants there but a neat little area to eat and shop.
La Fonda on Main- classic SA place with a great atmosphere that out of towners love
Things to Do:
San Antonio Zoo- possibly the best in the state
San Antonio Museum of Art- great location, architecture, and better works than expected for San Antonio
San Antonio Missions National Historical Park- Not as crowded as the Alamo and gives a better understanding of Colonial Texas.
Daytrips:
Enchanted Rock State Park- Fun hike, that isn't challenging. It's about 1.5 hours from downtown.
Fredericksburg- wine area, historically german town, WWII museum of the Pacific. A bit over an hour from downtown, can combine with Enchanted Rock
Corpus- oddball choice but good for a day trip. Selena Museum, Texas State Aquarium, USS Lexington, ocean fishing, an ugly water beach with decent sand. 2hrs from Downtown
8 days is a lot for SA, but plenty of daytrips options.