The entrance to Small Qingdao Island is beside Luxan Park, a China National Park, the park is inviting but be aware, the rocks beside the ocean are rugged and crossing them without athletic style shoes is not wise. Although taxis go out to the Island, most people walk from the main road. The admission is CNY 10. Several seafood restaurants are located beside the walk out. The word island is something of a misnomer since the roadway/ causeway is built on dirt and rock built up to connect the mainland to the island. This is also true of Maidao Island, on the east end of the city.
For some exercise and a scenic walk, this is a nice trip. It can be done in an hour. Benches are located with scenic views. On a clear day, there are photo ops for shooting the city, the beach area and the statue of a woman playing a lyre. be aware the sun will be on the back of the statue in the afternoon so for best shots, a morning visit is appropriate. The lighthouse itself is surrounded by trees and there is no unobstructed photo access. It does present some nice through the trees style shots in the fall and winter. There's also a path between the rocks in a sort of grotto that would be nice for some HDR photos.
A good view of the Chinese Naval Museum's ships, planes, and artillery is available from the side of the island toward the mainland. A visit to the museum can be combined with a trip to Small Qingdao Island. The entrance to the museum is about 50 meters west of the Luxan park and Small Qingdao Island entrance. The city wraps around most of the island. The main road is serviced by at least a dozen bus routes. Googling "Qingdao Bus Routes" will produce a page that allows one to enter the address of your location and the address you're going to. The page will tell you which bus routes service your destination.
If you have kids with you, be aware serious falls are possible for persons not following the paths.
If you own or manage Small Qingdao Island, register now for free tools to enhance your listing, attract new reviews, and respond to reviewers.