The 13th Lake area (location of Garnet Hill Lodge - good view from their property and a bar!) offers very nice hiking options many into the Siamese Ponds wilderness. Near the Lodge, you can hike up Balm of Gilead Mtn. Short with a good view.
Though quite a bit longer, a trip into Peaked Mtn pond, then up Peaked Mtn offers a nice variety (woods, streams with small falls, vleis, ponds) and a great view from open summit of Peaked Mtn. A bit steep above the pond but anyone can make it. Park at the N end of 13th Lake. The trail follows the W. shore of the lake before heading west (a left turn 200 yds. into the woods will take you on a new trail to Hour Pond - not on maps yet). Both 13th & Peaked pond great for swimming.
Not too far north (up 28N then W. a few miles on Northwoods Club Rd), you could hike into Blue Ledges, to get access to the Hudson River (cliffs on the S. shore here). Easy hike and you may see rafters go by if late AM.
Further N. from there is Vanderwhacker mtn. (Turn left W. just past the Boreas river) a 2.5 mile hike (steep after 1st mile) leading to a tower offering a view of many of the highest peaks in the Adirondacks.
If you have a more specific criteria, there are other recommendations. Have fun. ADK Central is the right book.