I'll second SEKI. But I'm quite biased as it is pretty much the only place I ever want to go (fortunately I grew up down the road in Visalia so didn't waste much time elsewhere).
The Alta trail is indeed a very enjoyable, quick and easy 2-3 day trip, and the view from Alta pk is awesome (in fact my avatar is me on top). Merhten, Alta and Panther meadows are all gorgeous along the way, and the views down the Kaweah canyon and up toward the GWD are awesome. From the summit of Alta you can follow the ridge to the north and drop down into Pear Lake and then follow the Lakes trail back to Wolverton. I would highly highly recommend this route to make it a loop, always more fun than an out and back.
A couple other fairly quick and easy trails in the area are the Lakes trail to Pear Lake (same trailhead as Alta trail - WOlverton), Jennie Lakes out of Big Meadows (dog-friendly as well), Eagle Lake out of Mineral King (can make a very easy x-country loop around White Chief Peak and down White Chief Canyon for a superb 2 night, or 1 night, trip). Or if you are looking to work a little harder, Sawtooth Pass is spectacular, a pretty easy summit from the pass gets you epic views of the Kaweahs and all the way to the Sierra Crest. Camping on the other side at Lake Columbine is spectacular and you can do the classic loop around to Little 5 and Big 5 Lakes, back around Black Rock Pass and over Timber Gap but that is pretty strenuous and is a minimum 3 very long days but most people do it in 4 or 5 or even 6 if you want to lay over and enjoy the excellent fishing at Big or Little 5.
Go to seki! Good luck,