Lake Sabrina is central to many great dayhikes, and is near North Lake and South Lake for more still. It can be crowded, but if you're not there most of the time, it's not bad. You can access the entire Sabrina Basin, then hop just north to the North Lake trail head to hit Lamarck and drop into Darwin Mendel, or hit Humphreys Basin and all it offers. From Humphreys, you could even head north and come out in the upper Rock Creek area. From south Lake you could have a couple of nice choices as well.
Rock Creek is nice too, as Chief mentioned. If the road to Mosquito Flat trailhead is open, there are several great easier dayhikes out of there as well.
Can't lose with Glacier lodge either, really.
Cant really go wrong with any of them, but Sabrina is central to many, many great hikes, with great scenery.
Have fun, and bring bug juice! They're prolly coming out in force soon!