From the end of the Spruceton Road on the Diamond Notch trail, you can reach the Diamond Notch Falls in 0.7 mile, and the notch's height of land in 1.9 miles which has some nice views to the south.
On the Pecoy Notch trail from Elka Park Road (south of Tannersville via County Route 16, and best access via Dale Lane) you can reach Dibble's Quarry in 0.95 miles where there are some interesting stone chairs, other stone constructions, and a great view of Kaaterskill High Peak and Roundtop. At 1.15 miles in a stream crossing with a small cascade, and at 1.55 miles there are some beaver meadows with a view of Twin Mt.
On the Platte Clove Road (County Route 16) south from Tannersville, near the top of the clove is the Plate Clove Preserve. There are two short trails south of the road (parking along the road). The Long Path crosses the Plattekill on a reconstructed 19th century style bridge. There are a number of interpretive signs beyond the bridge along the trail. Back at the road there is a short 0.2 mile trail that starts down the driveway of the ranger's house. It leads to an impressive 50' waterfall which should have a good flow of water currently.
Further east along the Plate Clove Road the Long Path leads north from a trailhead parking lot. Huckleberry Point can be reached in 2.45 miles using the Long Path (1.05 miles) and a side trail (1.4 miles). It has a very impressive view into the Hudson Valley and of the Platte Clove.
At the hairpin turn on Route 23A in the Kaaterskill Clove is a 0.5 mile hike from the parking lot to the Kaaterskill Falls. The trail can be icy and you have to walk along the busy highway for about 0.1 miles. The bushwhack climb up to base of the upper falls may be too icy to safely negotiate.
In North Lake State Park there are some nice views along the Escarpment Trail. From the trailhead on Schutt Road you can reach Sunset Point (1.7 miles) and Inspiration Point (1.9) miles. You could also take a short cut along the red then yellow trails that will save about 0.2 miles. And you could loop back around past the summit of South Mt (Hotel Kaaterskill Hotel site in a meadow on top).