If you can make the drive south to Corpus, Joe Cotton's is great. Whatever you do, stay away from Bill Miller's they used to be all over SA and are the equivalent of ordering BBQ at Subway or McD's.
If you can go north near Austin, The Salt Lick Barbeque is fantastic - been written up multiple times in Texas Monthly and Southern Living - great stuff - the open pit is a sight to behold. It's only about an hour north of San Antonio - well worth the drive.
Within SA, you might check out BBQ Patio or Blue Cactus. If you're willing to travel a little, then yes, certainly try out the Salt Lick in Dripping Springs or head East over to Lockhart.
A bit off the subject, but I can't believe Kreutz Market is not listed in the Lockhart section of that link. Like the other places listed, it is a legendary place for bbq in Texas.