Minx,
If you are into sport climbing, then consider trying a couple of routes on the Weeping Wall on Suicide Rock.
Serpentine 5.9 (Suicide Rock is on the other side of the road from Tahquitz Rock).
And, since you mentioned that you have 3+ weeks, you can easily just go back and forth between J-tree and Iddylwild (Tahquitz and Suicide--will be however much cooler than J Tree since it is at about 6000ft)
And like Alex mentioned, even the 5.4's and 5.6's on Tahquitz are great multi pitch routes.
Have fun!!!!!