WOW, that's a ton of time in the Gorge. That's what I like to hear!
There are so many ways to approach having a good trip in Linville Gorge, and certainly to each his own. I would suggest something similar to Michael, which would allow you to enjoy the leisures of car camping as well as a night away from the truck, with your backpack at the river.
If you have read a good bit on this site and it's companion site, Linville Gorge Yahoo Group, you know that some of the most strenuous hiking in the southeast can be found in the Gorge. That in mind, you should select only routes that you have both carefully studied and totally understand the difficulty of.
With the amount of time you have, you have plenty of time to get some base camp hiking done as well as a small backpacking loop or a down and out one nighter. Say you arrive Friday, camp near the road close to Conley, wake up Saturday and check out the Conley Cave, Petraus Point, Lost Dog Loop, and all or part of Rock Jock. That's a full day!
Sunday morning, if you're dead set on backpacking, head to Conley Cove Trailhead and descend to the river, probably less than 45 minutes. Head north on LGT to the bridge, cross the river, and head up Spence Ridge to either Little Table Rock or to MST and take either of them to Table Rock and then descend to and across the parking lot. Camp just beyond the parking lot on the right or continue across toward the Chimneys and camp just beyond there on the left. Set up camp and check out Table Rock with some remaining daylight.
When you wake up Monday, hit the NC Wall trail without backpacks, explore along the cliffs and make a loop back to camp using MST. Pack up and continue south along MST, descend to the gap, and back up to the head of Cambric Branch. Descend Cambric Branch to the river, crossing at the toe of the Cambric Ridgeline you will find a nice camp along LGT. (search for more about Cambric Branch Trail, as it can be tricky, also, no bridge, but you can make it easily by wading).
Tuesday morning make your way north on LGT back to Conley, ascend Conley back to the truck and find a nearby camp, possibly at old Conley intersection, or Lost Dog. Take it easy on Tuesday afternoon, maybe re-explore nearby portions of RJT, or take in the views at Wiseman's.
Wednesday wake up and pack up camp, maybe a quick stop at Wiseman's. Check out the falls if everyone is game. Then head into nearby Linville Falls and grab lunch at Louise's.
By the way, on the river crossing:
Mike and I crossed the river by wading at two very popular points on the 28th and 29th of May in 2008. The first being at the toe of Conley, and the second where MST first meets the river after descending from Pinnacle, just south of private land. Using records from the gauging station downstream, you can estimate whether conditions will be safe for crossing. Here is a link:
http://waterdata.usgs.gov/nwis/uv?02138500Looks like the max discharge for the days we crossed was just over 140 cfs.
-Lewis