Old Town Hall Road just North of downtown Conway. See below for directions I found online. You can find nice spots and you can tuck your car right next to.
Route 16N though Intervale, turn right onto Town Hall Rd. Cross over 16A at stop sign, continue up Town Hall Rd. Stay left when the road splits. Pass US Forest Service gate (locked off season). A few miles up this dirt road, take the first left (Slippery Brook Rd), cross over bridge. A mile or two later there is a campsite on the left on a brook, park over the bridge and walk back 100yrds. If that is taken drive to the very end of the road, hike back 100yds to a brook with a site right on the water. There are 2 or 3 more sites between these to in nearby fields, easy to find.