The Cowanesque River along Rt 49 upstream of Knoxville is quite heavily stocked and produces good early season fishing, albeit mostly put/take..
Pine Creek and it's tributaries are nationally famous..The creek itself is heavily stocked and many of its tributaries, such as Long Run,Asaph Run and Pheonix Run brovide good fishing for brookies, both stocked and wild..
The Genessee River is excellent on EITHER side of the border..As Crokit mentioned, it's a wonderfull trout stream from the PA border to Wellsville, but all three branches south of the PA border are great streams in thier own right...
If you want to branch out a little further south and west, there are dozens of great streams like Young Woman's Creek , Kettle Creek, and many others..
If you get your NY license, The Cohocton River upstream of Bath is a blue ribbon trout stream... It and it's tributaries hold plenty of beautiful wild and holdover browns..
If you want steelheads and don't want to drive all the way to Pulaski, there are many excellent steelhead streams flowing out of lake Erie, both in PA near Erie, and in western NY...
I could go on and on... Trout fishing opportunities within a fairly short drive of that area are practically limitless...