Wine tastings aren't what they used to be in terms of price. None are really cheap anymore. On the bright side, most will knock off a tasting or two when wine is purchased. A recommendation on wine tastings depends on what type of wine you prefer (if you know). Some ideas:
Pinot Noir - Walt Winery, just off the square in Sonoma. Our favorite Pinots in the area. We were white wine only drinkers when we first arrived in Sonoma and the Pinot Noir here was our "gateway drug" into reds.
Zinfandel - Wellington Cellars, north of town between Santa Rosa and Sonoma. They have a number of Zins including from vines planted in 1882, 1912 and 1924.
Cab and Red Blend - Three Fat Guys Wine, here's a curve ball for you. Just south of town, founded by three former Packers linemen, hence the name. They make a good red blend that's not too expensive (The Linemen) and a Cab or two that's good (though kind of expensive).
I might have some other suggestions depending on what you like (white, red, bubbly, ports, etc.).
If you want to combine a hike with wine tasting, you can check out Bartolomew Estate Winery. Beautiful spots to drink wine outside and the expansive property includes miles of hiking trails that lead up into the hills that surround the property. Plenty of Redwoods up there.