any suggestions on what to do with a day in Ashville? Suggested restaurants and activities would be helpful.

This may be obvious, but you must not miss taking a tour of Biltmore. It's really incredible, and hard to believe that anyone actually lived like this. There are gardens there that are absoloutly stunning. You can also take a tour of the Biltmore Winery. The estate was designed by Frederick Law Olmstead, who also designed NY's Central Park and Boston's Emerald Necklace.
If you have time, take a drive on the Blue Ridge Parkway. North of the city on the Parkway is the Folk Art Center, an interesting gallery that also has a great shop that sells local crafts. If you head south, you can go to Sliding Rock Park, also on the Parkway, where you can go swimming and slide down a small waterfall (they have lifeguards and changing rooms). Lots of fun on a hot day! Do you only have one day in Ashville? If you have more than one day, you might want to take a white water rafting trip on the French Broad River, there are a couple of outfits about an hour north of the city who provide trips. We did this a couple of years ago, did a half day trip and had a blast - it's intermediate whitewater, class 2, 3, and 4 rapids, enough to be fun but not scary.
You can make reservations for dinner (and I think Sunday lunch) at the Pisgah View Ranch in Candler, just outside of Ashville. It's a beautiful setting at the foot of Mount Pisgah, and they serve good country cooking family style. They have assigned seating times - I think the earlier seating is for Ranch Guests only, but available space at the later seating is opened to the public. Our only complaint was they give you too much good food, lots of different dishes on the table, and you feel compelled to overeat unless you have a lot of self control!

I have been there, too, several times.
I can add absolutely nothing to the answer you already have. Better than any tour guide book.

I agree that Biltmore is the thing to see. It can easily take a whole day, but if you go early and just take the basic tape-guided tour of the main house and spend some time in the gardens, you could still have a few hours to drive the Blue Ridge Parkway. Haven't been north of Asheville in a long time, but to the south there are many beautiful waterfalls. It might take you quite a while to reach some of them, but even if you don't get to many of the falls, the views along the parkway are wonderful. If you do go south, I highly recommend Whitewater Falls, Cullasaja Falls, Looking Glass Falls (just down the road from Sliding Rock), and Dry Falls, which are all either on the road or 5 minutes from it.

Asheville, please

The Biltmore Estate house, gardens, and winery are outstanding, as is the Estate's Stable Cafe. Depending on your interests (and careful timing), you might enjoy preceding your visit to the Biltmore with a scenic morning ride on the Smokey Mountain Railway.

Restaurants:

Max's Celebrity Deli Grill & Bar... terrific place downtown for lunch, great sandwiches, reasonably priced and great atmosphere inside or out.

Barley's Taproom... the place for pizza and beer, also usually a pretty happenin' nightspot after 8 or 9, again downtown (runner up - frank's roman pizza, couple locations)

La Caterina Trattoria & Vincenzo's... both have fabulous, fabulous authentic italian food. vincenzo's bistro downstairs is also a great place for live entertainment at night, very much the same atmosphere as piano bars in italy.

Fine Friends - good american bar & grill type food, but the north asheville location makes it a little tricky to find.

ps. if you aren't from the area, it might be worth asking around for a good barbeque place... i'm not a big fan of bbq so i can't help you there, but many carolina locals swear by it

If you have deep pockets, the Grove Park Inn just outside Asheville would be a lovely spot for lunch. The views are beautiful, the lobby is wonderfully historic and the food is great.