ship rock may be cold depending on day time temps....stone mountain isnt far...also little wilson and the dump...I'll let someone from the high country chime in. Also the linville gorge...not sure if the gate to Table rock is closed or not or what conditions are like. Could always check out the gold coast areas.
there's a ton of good climbing around, but not a lot of information. If your buddy doesn't know anything about it, I'd just stop by footsloggers in downtown and get directions from them. Most of the bouldering is relatively easy to find, and there are almost always people nice enough to show you around at the popular areas. If you want a rope, shiprock is trad, little wilsons is sport but I doubt you'll find it, the dump is really easy to access for sport, and linville gorge is where it is. Stone mtn is a little farther, 1.5 hours or a little more.
Tons of information in there on Ship and all the Linville stuff.
I guess it depends on what you mean by close...
within a 30 min drive of Boone you'll find world-class bouldering (Little Lost Cove, Blowing Rock, Grandmother Mountain) and Ship Rock, which could be a little cold this time of year but could be climbable depending on daytime air temps/previous moisture. There's also roadside sport cragging at the Dump (in the route database here I believe) which can be nice in colder temps.
Linville crags are anywhere from 45 min-1.75 hrs of driving from Boone depending on which one you hit up. If daytime air temps are cold, Shortoff Mountain has a nice southern exposure and can be quite warm. Lots of the Linville stuff is on the route database here as well.