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The park is accessed by the Lake Shore Bike Path, and a tunnel which passes under Lake Shore Drive at the east end of 55th Street. At the head of the park, seen immediately upon emerging from the 55th Street tunnel, is the David Wallach Memorial Fountain. This fountain was designed in 1939 by Elizabeth and Frederick Hibbard in the shape of a fawn, with drinking areas at human and animal levels. During the Cold War the park also housed a 150-foot (46 m) radar tower for the Nike Hercules missile defense system; it was dismantled in 1971.

The park contains a fieldhouse, built in 1937, the exterior of which is made of Lannon Stone from Wisconsin. Partly because of its view of the lake and cityline, it is a popular wedding and corporate event location. It competes with the much larger Jackson Park 63rd Street Beach House and the even larger South Shore Cultural Center as south side beachfront special use facilities. The frequent summer fireworks displays at Navy Pier are often viewed from The Point, especially on Independence Day, when large numbers of Hyde Parkers and other south side residents gather there. It neighbors the Museum of Science and Industry and the 57th Street Beach.

Water access is an important aspect of the Point's history of use. Swimmers, sunbathers, kayakers, and windsurfers use the Point's revetment to access the waters of Lake Michigan. In the summer months, the North side of the Point functions as a "rock beach." On the South side of the Point, distance swimmers swim South across the bay in front of the 57th Street beach. This has been the source of conflict with the Chicago Park District as swimming off the Point is not officially allowed. From time to time, swimmers have been ticketed for violating this rule. In 2003, the Chicago Park District offered to create an officially sanctioned deep water swimming area off the South side of the Point.