A few years ago I took some friends of mine to a wine trip to Livermore. They had wanted to visit Napa, but I've spent too much time stuck in traffic waiting to get to packed tasting rooms where the winery charges $10 for three little tastes, then offers you the option of tasting "reserve" wines for $15 more, and a futher "library" tasting for another fee. You can spend $40 in a tasting room trying wine without yet buying a bottle, which are themselves $40 and up. Plus you're fighting crowds.
Livermore has dozens of wineries, many that are smaller operations. Some of these I visited were literally in the garage of the grape grower. While you may not get astounding wines at every stop, you're bound to find a few great ones that won't cost you a ton of money simply because it was made in Napa.
One of the places we visited was Thomas Coyne Winery, a hard to find but worth visiting location in south Livermore. Specializing in Rhone and Bordeaux varietals, winemaker Thomas Coyne (pronounced "Coin") started making wine in 1989. The winery itself is on a hill in the middle of in an 1881 building built by French engineer Alexander Duvall. You can see Mt. Diablo in the background, and overall it's a really pretty place to try some wines.
All of the wines I tried tasted great, and I in particular liked the Petit Verdot. You can get these at Whole Foods as well.
The Petit Verdot, priced at $18, looked as black as night in the glass. On the nose, I found sweet jammy black fruit, and this followed in the mouth, as it presented ripe blackberry jam with a touch of vanilla and heat on the finish. Really thick mouthfeel, with the fruit flavors sparkling as a bright beam.
From the winery: "This little-known Bordeaux Varietal is normally reserved for blending to enhance color and body of the major varietals. The grapes came from a vineyard near Lodi in Northern California. After crush and fermentation, the wine was aged in American and French oak barrels for eighteen months. The wine is full-bodied in character with intense herbal flavors and rich oak finish."