For day hikes, start with trekking to Alberta Falls. It's only a half mile walk from the trailhead with lots of people around but it's so scenic you shouldn't pass it up. To extend this hike, keep going past the falls to Mills Lake, a nice place for a picnic lunch.
I'm not sure what the trail is called, but a second hike encompasses three lakes (Nymph, Dream and Emerald Lakes)with each one progressively more scenic than the previous. This is also a good one in which to pack a lunch.
And bring your camera.
You're gonna love this park.