Hiking/camping options?

We are planning a trip in June, but my daughter has also been asking me to go camping. We are getting a cabin for the week, but I was thinking about taking her camping one night while we're down there. I wondered if there were any trails with camping available where we can hike out in the afternoon/evening, find a place to camp for the night, then hike back in the morning. I kind of doubt it because of bears/wildlife, but I thought I would ask.

Assuming not, are there any good trails for a 1/2 day hike?