You'll want to start at the foremost vineyard in all of California wine country, the Robert Mondavi winery, and try the signature wine tasting where they will show you the two-story fermentation casks and teach you how to taste wine with some small appetizers at a farmhouse table. This vineyard is beautiful, and gives you a nice sense of the history and layout of the two valleys.
Robert Mondavi is about halfway up the valley, and from here you can go anywhere. If you keep heading north, you'll pass Beaulieu Vineyards, one of the larger and better known wineries, and after going through St. Helena, you'll end up at the Beringer estate. While this isn't the best wine in the valley, it's an amazing property with a good tasting and a lot of history, and integral to the character of Napa. They have some of the original wine-making equipment, and some top-shelf wine which will taste nothing like the Beringer you're used to drinking at home.
If you decide to skip Beringer, your next stop should absolutely be Silver Oak. They're a 'controversial' winery; they use american instead of new french oak, but in my opinion have some of the best Cabernet in the valley. The tasting is super fun and they are very generous with extra pours; you also get to take home a glass with every tasting.
At this point, you should probably stop for lunch, and there are a ton of great options. The oakville grocery has great sandwiches, and is a good place to stop if you just want to chill, and don't want a sit-down kind of place. If you're ok with sitting down, head to Yountville. This is where the famous French Laundry is, but our favorite by far is R+D kitchen, which is an awesome American Fusion restaruant with burgers, sushi, pasta, and more, as well as a great bar and wine list. Noah ended up here at the end of his first Napa trip, and uninentionally tried all of the appetizers. They're all great!
After lunch, you could head to Chandon (across the street from R+D kitchen) or go back north. Along the way you'll see places you've heard of (Cakebread, Opus One, Sutter Home), as well as some you haven't; Elizabeth Spencer has great white wines, Turnbull has some more bold cabs. This is also usually a good time to try something on impulse, so pick a place you think looks neat and give it a try!
If you're planning on heading into downtown Napa for dinner, you don't want to go too far north at this point, so you could pick another winery you see here or head into Napa and do some tasting. We really liked back-room wines in downtown Napa, they have a great tasting of local wines you can buy for reasonable prices, and it's a good place to find non-cabs that you can take home. For dinner, try Bounty Hunter (BBQ) or Carpe Diem wine bar. Or if you want something more casual, The Pear (southern comfort food) has really good chicken and waffles.
If you're planning to head back to Healdsburg and want to have dinner further north, then you could head to Beringer (if you haven't already), Sterling (great chardonnay), or Charles Krug. There's also the Castello Di Amorosa, which is a castle that has their own wine and we have heard is fun to walk around. There are plenty of places to stop for dinner in St. Helena or Calistoga on the way back, but our favorite is a little BBQ shack called Busters in Calistoga. If you want some fine dining and someone to reccomend a unique bottle of wine for dinner, the Harvest Inn is a great place to stop, and the Chef (Charlie Palmer) is one of the best in the valley.