If you want to hit multiple ones, your best bet is probably to head to the Fredricksburg area. The Fredricksburg Winery is in town and the folks there are very friendly. There's also several scattered around town.
I like Fall Creek Vineyards in Tow as a day trip, you can go to Cooper's in Llano for lunch.
Becker is best, and there is nobody even close to them in quality. I went to Texas Hills Winery, and the guy there was so proud of his wine and it sucked horribly. I second that the Viognier by Becker is best in the state - no other wine has that much complexity and flavor.
when I visited, I thought the people at Texas Hills were complete ********. completely different than Becker.
another great thing about Becker is they have a huge field of lavender. stuff smells great and they had it all over the tasting house when I was there.