The wife and I do short vacations all the time. We take about 4 days and find that generally gives us enough time.
We just got back from Napa Valley. We had a great time, but unless you can drive there and get a seriously reduced rate at some hotel, $1k budget is going to be rough. It will be difficult to enjoy the really nice restaurants, and that's part of the point of going to Napa, imo.
Some California alternatives that might be cheaper:
1) Carmel, Big Sur, Monterrey. All great locations, all within driving distance of one another. We love it there.
2) San Diego. Same as above. We love La Jolla especially.
3) Santa Barbera. There are some great ocean front hotels and plenty of wine tasting in the area.
4) Sonoma. Russian River has excellent Pinot Noir as you probably know, and you could drive to Napa just for the day. B&Bs are cheaper around Sonoma. It's also less crowded, there are a lot more trees, etc.
Where do you live? We like taking short trips in areas around us. There are islands, mountains, oceans, etc. All are within driving distance, so costs are greatly reduced.
You could also consider a short cruise, but the feasibility of that might depend on how close you are to a port.
That's all that really comes to mind. $1k makes it really difficult if you actually have to fly anywhere.