Kennedy Park is one of the best places to run on trails in Berkshire County. Unlike most trails around here, these have not been destroyed by 4-wheelers (because they aren't allowed). They are pretty smooth and not very rocky. Volunteers do a great job maintaining water bars and keeping the trails in very good shape. The trails "on the map" are great for running, beginner mountain biking, cross country skiing and snowshoeing. There are several more challenging single track trails that aren't on the map which are fantastic for mountain biking.
There are a large number of trails in this park. I highly recommend you take a map and consult it as you're going along or you might end up running around in circles as I've done on a couple occassions.
Warning: Horses are allowed. Always yield to horses!
Leave the Northwest side of the Arcadian Shop Parking lot on Woolsey Rd (#27).
Go straight on Overview (#11) up a hill.
Take a Left on Deer Run (#5)
Take a Right on J.D. Kennedy (#3)
Take a Left on Main Trail (#1) (this is broken pavement)
Take a Right on Picnic (#2) (You'll go right up a fence next to a green water tank - which should be on your left). This trail will lead you to a picnic area with a nice view. Leave the North end of the picnic area on a slightly rough and rooty downhill that leads past an old foundation.
Take a Left on Red Neck (#7)
Take a Left on Main Trail (#1) just after climbing up a steep rocky hill.
Take a Left on Pondside (#18) and go past the pond (it will be on your right). Just after the pond you will climb a steep uphill to Balance Rock.
Take a Right on Balance Rock Trail (#17). When you reach the top of this hill, the Rock will be a very short trip to the left. Head North on Balance Rock (#17) after leaving the rock until it intersects with Main Trail (#1).
Take a Right on Main Trail (#1)
Take a Left on Weaver Olympic Trail (#20)
Take a Left on Aspinwall (#12)
Pass Nose and continue straight on Aspinwall (#12) descending down a steep hill the rest of the way back.
Take a Left on Woolsey Road (#27)
When you're done, stop in at the Arcadian Shop. Have a coffee and a snack, surf the web and buy some gear! Or just go in and talk with the people there! It's a great store.