The Point Picnic Area is the day-use spot at the very end of the road on The Point, a wooded peninsula that juts into Lake of the Arbuckles just northeast of Arbuckle Dam in Chickasaw National Recreation Area. The National Park Service manages the lake and the land around it, and its swimming page names this picnic area as one of the most popular places on the lake to get in the water. Some swimming-hole sites list it under the informal name Arbuckle Swimming Point. Lake of the Arbuckles is a reservoir of about 2,350 acres with 36 miles of shoreline, and it doubles as a water supply for Ardmore and other towns to the south.

The Point sits about 5.5 miles southwest of downtown Sulphur. From town, head west on Oklahoma 7 and follow the park signs south onto the paved road (Charles F. Cooper Memorial Drive) that runs down the peninsula past The Point Campground and the turnoff for The Point boat ramp. Keep going until the road ends. A paved parking lot sits right beside the picnic tables, with grills, trash and recycling bins, and the lake on three sides within a short walk.

Expect open lakeshore rather than a groomed sand beach, with no lifeguards; the park says plainly that all swimming is at your own risk. Its brochure asks lake swimmers to stay inside boat exclusion areas where they are marked. The shore drops off into a deep reservoir (the state wildlife department lists a maximum depth of 82 feet), so non-swimmers and kids need a life jacket and close supervision. Unlike the cold spring-fed creeks elsewhere in the park, the lake warms up through an Oklahoma summer. During the busy season the park tests bacteria levels at its most popular swimming spots and posts the results on its Bathing Beach Monitoring page, which is worth checking before a visit.

There is no entrance fee for Chickasaw National Recreation Area, and the picnic area and parking at The Point cost nothing. The park charges only for camping and for boat launch permits at the ramps. Outdoor areas of the park are open all the time, though swimming after dark is discouraged by the park.

The main hazard here is boats. Lake of the Arbuckles is busy with motorboats, water skiers and personal watercraft in summer, and swimming is not allowed near boat ramps, courtesy docks or fishing docks, so stay close to shore at the picnic area and away from The Point ramp up the road. Never swim alone or from an unanchored boat. After heavy rain, runoff carries logs and branches into the lake, and the park warns boaters to watch for floating debris; swimmers should look before jumping in. Road and parking lot work can close areas of the park for short stretches, so check the park's conditions page before you go.

The Point Campground, with 55 sites split between an upper and lower loop, is a short drive back up the road, and a ranger station operates on The Point. Two short paths, the Lakeview Trail and the Fishing Rock Trail, follow the shore near the picnic area, and bass, crappie and catfish fishing on the lake is rated among the best in the state. For cold spring-fed creek swimming instead, Little Niagara and the Travertine Creek pools are in the park's Travertine District on the other side of Sulphur.