My top 10 suggestions (in no particular order):
(1) You should go ziplining! Check out Navitat.com.
(2) You should spend a day exploring downtown Asheville. Lots of interesting shops, and, as others mentioned, great food.
(3) Take a drive and/or hike and/or picnic on the Blue Ridge Parkway. Some of our favorite spots are Craggy Gardens, the Pink Beds, Graveyard Fields, Mt. Mitchell, Devil’s Courthouse, Mount Pisgah, and Looking Glass Falls.
(4) In August, I’m sure there will be lots of local festivities going on. Check out the Mountain Xpress (either online or pick up a paper copy once you get to town, they’re free and available almost everywhere esp. in restaurants).
(5) Check out the River Arts district. I recommend breakfast at Clingman Cafe and lunch at 12 Bones and strolling through the artists’ studios in between.
(6) Go to the Biltmore House. I think you can get a discount on tickets if you buy them at an Ingles grocery store (the main grocery in town, they are everywhere).
(7) If the baseball team is in town, catch a game: http://asheville.tourists.milb.com.
(8) Drive to Hot Springs (about 45 min.) and take a dip in the natural springs. You can take food and have a nice, romantic (and fairly cheap) date. I would recommend making reservations since August is pretty popular.
(9) Take the segway tour, as someone else mentioned.
(10) Take the Brews Cruise to visit the local breweries.