Well with 4 full days you could hit up:
Gooseberry.... easily spend a whole day up there and then some...
Little Creek.... better part of a day.. maybe a shuttle for a ride "down" the JEM at the end of the day for a smile that will last all night.
Rockville Bench and Guacamole - Guacamole is basically a "Gooseberry Lite" (You could do just Guacamole for a sort AM ride on your last day) then four hours or so in Zion Natl Park.... you're right at the entrance.
JEM, Hurricane Rim, Goulds loop - Starting at the "bottom of the JEM, this is a great day 24 miles or so with some good climbs and a rippin ride down teh JEM and along the Virgin River at the begenning and end... if you don't like exposure the first and last mile or so will pucker your ass.
Sidewinder/Barrel Roll/Rim Reaper, Rime/Rambler/Rim Rocker - this could be a full day and is a fun trail network. Do just part of it and then do ZEN or Bearclaw Poppy as an alternative
Bearclaw Poppy/ZEN - Nice ride
Prospector to Church Rocks loop - A nice out and back.. also a candidate for a short day five before you go ride home.
Plenty to keep you busy for a week!
Camping Options:
Goosebery - Primitive (They have one bathroom) free
Little Creek - Primitive free
Zion Natl Park - Fee
Sand Hollow State Park - Fee
Quail Hollow State Park - Fee
Mesquito Cove on Virgin River along SR9 between Virgin and Springdale - Primitive free
Virgin River RV Park in Virgin on SR9- Private Fee but super nice. Right on the river..pool, hot tub, premiuim... but IMO worth it.