If you want immediate and early entry into Independence Hall you must arrive early. But if your ticket gives you some time to spare, stop by the exhibit in the center, the cafe or gift shop. Just north of the center is the National Constitution Center. In the between the center and Independence Hall is the Liberty Bell Center and the President's House Site. Definitely and highly recommended is to pick up a National Park Service map to find the many sights within the few blocks around the center. I would suggest shopping at the gift shop for official souvenirs (below is a photo of the shop's decorative plate) after you've visited the nearby attractions.
The Independence Visitor Center is located at 6th and Market Streets in Philadelphia. Opens daily from 8:30am-6pm; from Memorial Day to Labor Day 8:30am-7pm. Visit independencevisitorcenter.com for more info.