Downtown Asheville is easily walkable — most of the central attractions are within a fifteen-minute walk of Pack Square. The River Arts District is a short, mostly flat walk or bike ride along the new greenway, but uphill on the way back. The Biltmore Estate, the Grove Park Inn, and the arboretum all need a car or a rideshare.
The city's ART buses are useful but not frequent; check the schedule before relying on them. Rideshares (Uber/Lyft) are widely available. For day trips on the parkway and into Pisgah, a rental car is effectively essential. Bike rental is easy in the River Arts District and along the greenway.