I live in San Antonio and I love to walk the Riverwalk. Sure, it's touristy, but it also isn't when you look at the walls, the bridges, the landscaping, the trees. I find it very relaxing at times. The newer parts of the Riverwalk - the mission reach and the museum reach are nice too. Walk up to the Pearl and enjoy dinner or lunch at one of the restaurants there. La Gloria is great.
My suggestions for what to do and see really would depend on the time of year you are coming. You might need a car if you want to do anything that isn't downtown. But if you can do a lot just staying downtown.
Do you want outdoor, inside, history, shopping, or what?
Go to the Alamo, but also don't leave out the other missions. They are beautiful and each ha their own history. They are strung out on the mission walk, but it's a 13 mile hike, so I would suggest renting a bike (b-cycle is good) or renting a car.
South of downtown is an eclectic area where you can find some interesting art, decorations, and some great food too. Check out the Blue Star Complex and be sure to eat at La Tuna across the street. Bottlecaps are used as gravel here....
Take in the IMAX Alamo movie at RiverCenter Mall. It will get you into the history and it's a great way to avoid the heat of the day.
The Botanical Center is very pretty. You can take the bus there. Also, check out the zoo if you like animals. Next to the zoo is Sunken Gardens, which I love. They've really done a lot of work there and it's gorgeous. You'll need to take the bus to either of these.... Breckinridge Park is the area where these are located.
Downtown - while you are on the Riverwalk, sit a spell at Arneson Theater and walk up to La Villita - a bunch of shops in the old part of San Antonio. Or eat at Casa Rio on the Riverwalk. It's one of the oldest restaurants on the River, and it's iconic umbrellas are the ones on the postcards you usually see. Schilo's Deli is one of my favorite places to eat downtown too. Great food! If you want something more upscale, make reservations at The Palm, Fig Tree, or Il Signo (that one is at The Pearl)
Go to El Mercado/Market Square for a taste of Mexico. There are so many shops there full of Mexican items it's just like Mexico. If you've ever been on a cruise to Mexico, it's just like the port shops, only more. Eat at Mi Tierra's or La Margarita. A little across the freeway is Pico de Gallo. All are great, but my fav is La Margarita's. Take the trolley to these.
Hemisfair Park is a nice spot with playgrounds for kids. The Witte Museum has some good collections, take a bus to this. Also the McNay for artwork. Or go to the Institute of Texas Cultures for a bit of history on the area and it's people.
If you decide to get a car, there are other things to see - the hill country is full of great sites like the LBJ historical area, Fredericksburg, Enchanted Rock, and Natural Bridge Caverns.
The Painted Churches on the east are a good day trip. It's a set of about 20 churches built by Czech and German immigrants when they settled around Schulenburg. Very pretty and interesting.
Hopefully that will give you a start. Once you narrow your dates and desires down, ask again and I can help you.
