For Asheville, I would recommend the BRP for sure. Asheville is in the valley, so starting on the BRP near town will require a long climb in either direction. Also, the further you get away from town the less the traffic will be. Will you be there on the weekend or during the week? How fit are you?
An out and back is what works most often on the BRP though there are longer loops that can be made. Since you only have a half day I would suggest driving up to a higher elevation to start your ride. That way you get the vistas and the cooler temps. I can offer some places to start a ride if you let me know how far you want to go (but all of it is good).