Some of the places I have been to and have liked. Unless noted all websites have links to maps. The updated NJ Trail Association website (link) is a great resource for finding trails.
A short distance from the GC or Lawrence apartments. You can get a great view of the sunset at the western end where the woods turn into cornfields.
Walking along Lake Carnegie is especially nice heading north on the Towpath from Harrison Street. Pretty much completely flat. There are always people with billion dollar cameras taking pictures of ducks at the bridges by Millstone apartments.
Witherspoon Woods/Mountain Lakes
I always get lost here.
A bit outside of town:
Not very popular (not sure why) and easy to get to.
10-25 minute drive out of town:
Lawrence-Hopewell Trail, and Mercer Meadows/Rosedale Park (link with directions but no map)
The Lawrence-Hopewell trail is great for biking, though lots of it remains unpaved. Everything is very well signed with lots of different spots to start a walk. Both Mercer Meadows and Rosedale Park are quite open and both are nice places for seeing the sky if you need a break from all the trees.
You can make a nice loop by walking on Fiddler's Creek Road.
Lots of wineberries in June. Usually lots of people.
45 minutes out of town:
The trail off of Pine Hill Road is very nice. Some of the trails have no bridges so you will have to ford if you want to keep going. Wickecheoke Creek is beautiful.
At least a day trip:
A big area with lots of great places to hike. Really pretty creeks and waterfalls and the view from the ridgeline looking down on the woods and farmland is incredible. I have not explored much of the Water Gap but the trails starting from the Pocono Environmental Education Center and the I-80 trail head between Mt. Tam and Mt. Minsi are great.
Wharton State Forest (no great online map, though there is a map for the 50 mile Batona trail through the Pine Barrens.)
Easy to make loops starting out of the visitor center at Batsto Village. I have only been during winter but I am guessing there are lots of blueberries in the summer.
Nice walks in the woods and above the Lehigh Gorge and a very cool boulder field leftover from the last ice age.
A narrow 20-some mile park that follows the Lehigh River Gorge with a walk/bike path. Dramatic hills and a beautiful river the entire length of the park. If you park in Jim Thorpe, PA at the southern end of the park you can rent bikes, get a shuttle ride to the north end of the park and bike 25 miles of gentle downhill back to your car.
Marginal day trip, likely better as a weekend trip. A seven mile loop trail takes you past 22 waterfalls. Amazing.
Built around the Youghiogheny River Gorge with lots of beautiful woods, streams and waterfalls. The Jonathan and Meadow Run trails are very nice. Frank Lloyd Wright's Fallingwater is a few miles down the road. The smaller Bear Run Nature Reserve (site) also has some nice stream-side hiking. Ohiopyle is the southern terminus of the Laurel Highlands Hiking Trail (site).
Worlds End State Park and Loyalsock State Forest (the public use map is the most helpful)
The 60 mile Loyalsock Trail goes through the state forest. This entire region is really pretty. Beautiful creeks, streams and woods. When you get to a viewpoint you can see rolling green hills going on forever. Probably incredible when the leaves are turning.