If you're short on cash during your visit, no worries. You don't have to go to the Biltmore to have a good time. There's plenty to see in Asheville that won't cost you much money.
1. You're right by the Blue Ridge Parkway, which offers hundreds of miles of gorgeous scenery and hiking. Of course, you're not going to be able to go the full length of this road, but you can hop in your car and go for a very pleasant drive, stopping at viewpoints along the way or with the plan to park and hike in the woods. We enjoyed a short drive through tunnels, along the curving road, and I could imagine just how brilliant this would be in the autumn when the leaves are on fire.
2. The Thomas Wolfe Memorial House is located in the heart of the city at 52 N. Market Street next to the Renaissance Hotel. Faulkner was a fan of Wolfe's, and he is another important American writer from the South. His first and probably most famous novel, Look Homeward, Angel is set in Asheville and features many real landmarks such as the home though it's named "Dixieland" in the book of fiction. You can tour this home for $1 (!!!!) every day of the week except Monday. Unfortunately for us, we stopped by too close to closing on Sunday afternoon and could not go inside. However, if you happen to be here when the museum is closed, there is another option that will give you a brief overview of the home's history. There's a cell phone number posted beside the house sign that lets you call a narrator who offers a recorded overview of the significance of the house. There is no charge for this other than regular cell phone charges for the call.
(I ended up touring this attraction on my second trip to Asheville, and this was a wonderful thing to do. The tour is a little under an hour, so it gives you a good feel for the author as well as the boarding house. My friend who was with me was not familiar at all with Wolfe, but she liked seeing things like the cherry pitter in the old-fashioned kitchen. There's something for folks interested in architecture/history and literature alike.)
3. The Basilica of St. Lawrence located at 97 Haywood Street is a gorgeous church to see on the inside and worth a visit. A living Roman Catholic church, it is not a museum. However, if you have any interest in architecture or religion, it's worth a look. Notice the exterior is in the Spanish Renaissance style. You can go on-line and get information about the interior before you visit so that you can look for special features. Of course, one needs to be respectful of times when mass is in session, but we were able to go into the church on a Sunday between services. The stained glass windows are gorgeous. Most of these were made in Munich, Germany. The oval shaped ceiling is an amazing thing to see. You can make a contribution if you'd like to help with preservation of this building, but entrance is absolutely free. We lingered here for about twenty minutes. There is a gift shop inside as well though it was closed on our visit. It goes without saying that if you are a Christian--especially a Catholic--you would be welcome to worship here as well during your visit.