Wherever you end up tasting, I would call today and set everything up. Most of the better tastings/tours book up weeks if not months in advance. That being said, you might get lucky with some last minute cancellations.
Just to list a few of many wineries not listed by Cecil:
Schramsburg- Sparkling wine, one of the most visually impressive tours I've been too. Literally 2 million bottles of sparkling wine stacked up in caves that you walk through.
Hall Rutherford- Primarily Cabernet and some pretty decent ones to boot. The tour is also visually appealing as they have a tasting room in their caves with one of the neatest chandeliers I've ever seen (they call is Chilean Red).
Stony Hill- Primarily white wines; this tour is very intimate as you literally walk the grounds with the owner and can ask anything and he has an answer. When we were there, the winemaker was pumping over a small batch of Syrah; we got to taste the juice and chat with the winemaker for a while. Lastly, the view while tasting is beautiful, you are up high on the West side overlooking the Valley and Howell Mountain on the opposite side.
Chappellet- Another primarily red winery located up Prichard Hill. When I was there, they were harvesting their Prichard Hill Cab grapes. We got to see the whole process up close; very cool. They were also in the process of maceration with some other blocks of the Prichard Hill grapes; we got to grab some grapes and juice and taste that too, tons of tannins. I think timing and luck of being there for harvest made this tour stand out.
Del Dotto- All reds, small cave tasting, all tastes are thieved out of the barrels, cool experience and if you're not careful will get you pretty lit up.
I'm sure BSD can chime in with some great ideas too.
As far as food, I highly recommend
Auberge Du Solei for lunch, request a patio seating and enjoy the amazing views of Rutherford.
Hope his helps you create an awesome Napa experience.
*Edits- I think I figured out the pictures, they are compressed and are not as clear or vibrant as I would have liked but it gives a good idea of the views.