Not many good options for multi overnight trips in New England, but plenty of one night runs. If you don't mind a portage or two (dams/water falls) that will add numerous runs. Although if you are spending a lot of time fishing, you won't be making the miles.
Vermont has great trout fishing for brook trout, stocked rainbows and Browns, and some stocked jumbo rainbows in the 20"-24" range. There are tons of small rivers in Vermont, but you'll need heavy rain to boat, and that will make the fishing not so good. The White River in Vermont has a long stretch of water, mostly flat quick water class I, with some ledgy class II. Or class III if you start up on a tributary. White River is almost always boatable. Fish, trout and small mouth bass, maybe a pike or walleye if your lucky.
Another great Vermont option is the upper portions of the Connecticut River, great fishing. Multi fish species, decent scenery, bald eagles.
Maine has a few options, but your looking at a 3 to 10 hour car ride. Androscoggin from New Hampshire into Maine. Kennebec and dead Rivers in central/southern Maine. Or if you want to drive to the north woods Penobscot, matawamkeg, allagash, st John. Google Maine River map and look at images of maps. Watch out for moose while driving.
Massachusetts, a good bet would be the Deerfield River from fife Brook dam to the east Charlemont boat launch, 23 miles. Class 1-2 with one class 3. Need to rely on dam releases (every day, except the first weekend of June for a fly fishing tournament). Lots of fresh stocked rainbow trout in the 12-14" class, some holdover Browns and bows topping at 20". Record fish in the 30" class do get caught, but unlikely. There are lower stretches of the deerfield that are also decent options, but less whitewater. need to be discrete with camping, or camp on islands. If logged like 10000 miles on the Deerfield in the past decade mostly on the fife Brook section, but I've paddled it from headwaters to the mouth and camped at multiple spots.
In Connecticut, the only real option is the housatonic from Ashley falls to Kent. Good fishing, but not worth it if you have better options.
No good rivers in Rhode Island.
New Hampshire has small rivers like Vermont that you'll need rain to run, and have to make several portages to extend into multi overnight.