St. Regis River State Forest
The St. Regis River State Forest is 928 acres north of St. Regis Falls and the Adirondack Park. It is crossed by an old rail grade that provides easy access to the back country. Three blazed trails are shown on this map. Red trail is 6/10 mile, along west shore of St. Regis River. The 1 mile yellow trail is access from the Old Rail Grade, to provide access to east shore. The St. Regis School trail is 3/4 mile natural trail loop from school to south. More details from NYS DEC on St Regis State Forest.
Elephant Head Trail
The Elephant Head Trail overlooks Lake Titus which is south of Malone. The 1/2 mile, modestly steep trail overlooks Lake Titus, although in the winter one must hike back about 2 miles from NY 30 along Elephant Head Road. There is a nice description of the hike with many photos over at All Trails. https://www.alltrails.com/trail/us/new-york/elephants-head-trail
Deer River State Forest
Deer River Flow
Rimrock Overlook Trail
An alternative to going to the top of Rim Rock is to go for a nice stroll up the mountain via an old woods road from Kinzua Beach to the summit.