The trail is mostly gravel and you can use a road bike however, you should run 28mm tires with no more than 80 lbs. 32mm is more appropriate, though many road bikes will not take a 32 tire. Cross bikes work great on this trail.
A good place to stay is the Knights Inn in Galax, as it sits on a hill overlooking the city and is only about a quarter mile to the NRT hub entrance (right down 221 before it crosses the river). The motel cost is very reasonable and the place is plenty decent. Ride from the hub entrance to the Shot Tower and back on Saturday. Spend the remainder of the afternoon relaxing in Galax and eating barbeque. Go to the Blue Ridge Music Center on the Parkway (about 8 miles South of Galax) Saturday evening and enjoy some good bluegrass music. They have concerts of some type every weekend. On Sunday, drive to the Shot Tower and park. Ride the remaining trail to Pulaski and return, then drive home. You will have covered all 59 miles of the trail.