Some more photos here.
Trails, beach, dog beach, picnic areas
Info: This is a nice little state park (free) with bathrooms, a beach, a dog beach, picnic areas, bathhouse, ruins of an old inn, and a couple of nice trails of some historical interest. You can see Nine Mile Point Nuclear Power station from here.
Directions/Location: Take the Mexico, NY exit (Exit 34) off from Route 81, onto Route 104 toward Mexico (West) for just under 6 miles. Turn right (North) onto Route 3 (Scenic Ave.) for 4 miles, then turn left onto Route 104B (West) for about 1 and a half miles. Then turn right onto Mexico Point Dr W and you will find the park at the end of this dead-end road.
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Geocache(s) from Geocaching.com: GCK6DK [N43 31.478 W76 15.443]
Trail Distance: A few miles.
Date/Time Open: Dawn to Dusk
Mountain Biking Allowed: Yes
Hiking/Walking Allowed: Yes.
Cross-Country Skiing: ?
Pets Allowed: Yes
Built on Former Railroad Bed: No.
Rest Rooms: Yes, with running water and sinks.
Drinking Water: Yes, drinking fountain.
Special Instructions: Free admission even though it is a state park.
For More Information: Contact State of New York Parks