Congrats!! Kayaking is a great alternative when trails are less than ideal. Sit-on-top? or Sit-inside?
Some suggestions (all of these are, coincidentally, have good MTB'ing nearby, so bring 'yer bike if you want to make a day of it. I sometimes do that (e.g. ride at Jungle, kayak at Monksville down the road; Ride at Wawayanda, Kayak at Wawayanda, etc).
Nearest to you:
Splitrock for sure
Cranberry Lake (launch off the public dock off the Sussex Branch trail...not the private dock next to it)
Further north:
Lake Wawayanda
Monksville Reservoir (North section is cool...head northwest to the stream that feeds in from the ruins of Long Pond Ironworks and go for a hike among the ruins before heading back through the sunken forest). Don't be surprised to see
@Kaleidopete up that way on his fattie ;-)
Shepards Lake (Ringwood) but it's a bit small for the trip up there
South of you:
Round Valley (clearest water in NJ)
D&R Canal (from 6MR south to Griggstown is good stretch between the inevitable bridges)
Chimney Rock (Washington Valley), though it's a bit small, and I haven't figured out an easy way to portage into it, but I have seen kayakers in there
Carnegie Lake (Princeton)
Clinton Reservoir (near High Bridge)
West:
Delaware River (Class 1, maybe some 2)
Lehigh River (Class 3...sit-on-top or actual whitewater boat recommended)
As for how to carry them...I use J-style bars. As I get older I might consider splurging on the "Hull-a-vator" hydraulic assist racks to spare my back, but they are pricey at $400+ each. A trailer makes loading a snap (you can keep the boats on the trailer for the next adventure), but the downside is you need space for it, plus not all put-ins have enough parking for a vehicle with trailer.