Welcome to the forum!
I assume you're backpacking? It's very difficult to get a reservation at the camps, but once you have your wilderness permit you can request a "meals only" plan at the camp if you're so inclined. It's a bit pricey but you don't have to take so much food or worry about preparation.
Assuming your kids like outdoor stuff, I would recommend at least two nights and probably 3. It'll take you the better part of the day to get there and set up camp unless you have chick-on speed (search this forum for chick-on).
Get a good map if you haven't already done so. I recommend Tom Harrison maps but there are others out there.
Regarding hikes, head out toward Evelyn lake and beyond to the saddle. Spend some time taking in the views.
Head up to Townsley lake, then maybe climb up to basket lake or go cross country to Evelyn
Head up to Vogelsang pass, passing Vogelsang lake, and take in the views. Climb up Vogelsang or Fletcher if you think it's safe for your kids to do so. Remember, boulders do fall down from up high so be careful.
I'm not a fisherman so I can't recommend any of the lakes but maybe some others will chime in. IMO, Vogelsang is one of the prettiest areas in the Sierra.
A quick search turned up this link:
http://tedmuller.us/Outdoor/Hiking/2011/110818-VogelsangPass.htm