Restaurants: Barley Swine, Torchy's Tacos (seriously. SERIOUSLY.), Trudy's, Any of the food trucks on S. Congress, Snack Bar, Amy's Ice Cream, Home Slice Pizza, Magnolia Cafe, Shady Grove, Chuy's... this list could get long.
BBQ: Drive out 71 West toward lake Travis and go to Opies. Flat out EPIC. Salt Lick is pretty good.. but IMO overrated.
Lime Creek Rd on the East side of lake travis is a blast to ride.. probably the most twisty road I've ever been on. It is paved though.
The green belt is great for easy hiking, and right in town. Enchanted rock for hiking as well, though it is an hour to the west.
I haven't been out there but I've been told that the Lost Maples area is incredible if you catch it when the leaves are turning.
This is a great city to visit.. if you need any other tips let me know.