What distance do you do? Five miles per day, ten miles per day, fifteen miles per day?
On the Yosemite National Park website, there is a list of most of the major trails in the park, and it shows which ones have the wilderness permit reservations booked up. You don't absolutely have to have a permit reservation, but it often helps if you are trying for a weekend or a popular trail. Otherwise, you can simply go to any of the wilderness permit stations and ask what is available within the daily quota.
Let's see. There is the Old Secret Lake, the New Secret Lake, and about a zillion others.
If you are looking for a simple one day hike in, overnight, and one day hike out, you won't have such a tremendous selection.