Since August, 2011, I've been living near downtown Hudson with the Assabet right out my back door. One of my first acts was to grab a low-cost kayak and start exploring.
I'd recommend a quiet but rewarding trip downstream, putting your kayak in at Gleasondale. From Main Street leading east out of Hudson, take Route 62 heading northeast approximately one mile to where a bridge crosses the river, near an old mill on the left hand side of the road. You can pull your car out just north of the bridge, on the right, where a short path takes you down to the water's edge.
For the next five miles, you'll enjoy some very scenic paddling through the Assabet River National Wildlife Refuge, with not a lot of development around. The river passes at least one big island where model plane enthusiasts like to fly their electronically-controlled contraptions, as well as running by a big estate where a local collector likes to hangar his vintage World War II airplanes. But much of the journey feels secluded, with not much more than the occasional duck blind to show the touch of human presence. You'll likely spot some mute swans and other wildlife.
Before arriving at the Ben Smith dam in Maynard, there's a pull out on the right where you'll find a small park called Icehouse Landing, adjacent to the town's recycling and "transfer station." This is the end of your downriver trip, since you definitely don't want to go over the dam, which is well-marked and barricaded with floating orange barrels.
I threw both my bike and my kayak into my Honda Civic, then locked the bicycle at the park in Maynard, driving the boat back to launch at Gleasondale. It's about a five mile bike ride, following Route 117 northwest to Stow, then back down Route 62 southeast to return to your car and starting point. Makes for a nice round trip adventure.
I recommend the Assabet River Pocket Guide, published by OAR, Organization for the Assabet River.