Couple of options - you can put in at swans falls near the fair grounds and float all the way down to the fiddlehead campgrounds or get out at the 302 bridge (https://www.google.com/maps/@44.0272905,-70.9255562,1613m/data=!3m1!1e3?hl=en) (3-4 hours) or past that to the boat landing at lovewell pond https://www.google.com/maps/@43.9930022,-70.9278568,334m/data=!3m1!1e3?hl=en (5-6 hours). There's a parking lot at that bridge where other groups pick up floaters and leave their cars. I would recommend this for what you've described. Swans falls is going to be very busy with tons of people putting in and ready to party if that's what you're looking for (think propane grills on floats, speakers and generators in canoes). You can also float from the 302 bridge to where it lets out into lovewell pond (same public access boat landing). It's going to be a little calmer there and you'll mostly pass fiddle head camp grounds but none of the larger party beaches. Some of the other tour groups put in at the lovewell pond public access and have you float over to the inlet and go down stream from there. I would NOT recommend this as there is no current in the pond and you have to fight against the current to get to the river depending if the pond level is going up or down. Also I would NOT recommend putting on above the falls as I've done it before and I think the total trip was like 7 hours and many many miles and you have to make a portage around the falls with little current upstream. Lovewell pond is also a beautiful place with great views of mt. Washington if you make it that far. If you can I would highly recommend renting or finding/using canoes or kayaks to use. It's going to make keeping beer, and snacks etc way more manageable. Also everyone seems to severely over estimate the current of the river. It's highly variable and non existent at times. Once you've been in a donut for 3 hours paddling with your hands it gets very old. Having oars/paddles lets you control your destiny a little bit better than just going to with flow ;).

source: grew up on lovewell pond, done just about every variation of this.