Michael B.
Yelp
It sounds strange, but if you're visiting the San Antonio River Walk, you're 99% likely to visit the Rivercenter whether you like it or not.
The RC is a block-long mall which sits astride the eastern end of the River Walk. You'll be going down into part of it if you want to catch one of the boat tours (which you really should). The RC is also smack in the middle between the River Walk and the Alamo, which is really good - or bad - depending on how you look at it.
The Bad:
As a shopping experience, it's a decidedly mixed bag. There's a food court, a smattering of restaurants, a strangely unfocused mix of stores, and lots of weirdly placed escalators. Personally, I'd skip both the up-and-down scale franchise stores and visit the San Antonio specific gift shops like Texas Treasures.
Regardless of how you feel about the shops, they are good at one thing: attracting people. Beware of crowds on the weekends!
The Good:
Parking in the 'Pink' Garage (aka the River Center Parking Garage off of E. Crockett Street) is a major plus. Yes, you have to pay - but it's easily the most central spot between where you can catch the boat tour and walk to the Alamo. Also, having an air-conditioned inside mall to walk through is a godsend when it's raining or 100 degrees outside.
As a dining experience, I like the different options available depending on your budget. Pick the specials at the food court and you'll do fine when being thrifty. There's several chain outlets of sit-down restaurants for the middle grade. Finally, there are at least two steak houses (Mortons and 1718) and several higher-end restaurants on the River Walk itself within walking, water-taxiing, or cab-ing distance.
Like I said before, you probably won't be able to avoid the RC, so enjoy the highlights and smile - you're in San Antonio!