My two favorites are a bit outside of town. I highly recommend the Cascades in Giles County. It's probably my favorite hike of all time. You follow a pristine mountain stream up a gorge for about two miles and end at a spectacular waterfall. It's probably about an hour drive from Roanoke. If you go it's $3 to park unless you have an annual federal lands pass.
Another one I really like is Bottom Creek Gorge on Bent Mountain. You can find information on the Nature Conservancy's website. It's around five miles and has virgin hemlock forest, remnants of an old settlement, another beautiful mountain stream, and the second highest waterfall in Virginia (although nowhere near the volume of the Cascades even though it's taller.) It's not as much elevation change as the Cascades.
The trails on Mill Mountain are nice for city trails but don't really have any special features other than the overlook at the star. With such short time, I'd recommend driving up to the overlook and spending your hiking time at some other destinations. Nothing wrong with them, but they won't give you a feel for the true beauty of the mountains around here. Wear good boots or shoes as the trails are rocky on Mill Mountain and are sharp. I could feel every one of them the last time I was up there - even through my hiking boots.
You'll also have easy access to the Roanoke River Greenway from your hotel. It's a paved greenway that runs along the river and is nice for a walk or bike ride with river views most of the way.
Edited: 10:53 pm, September 10, 2011