With only one or two exceptions, avoid roads in New York and surrounding states parkways. Probably the most notable exception is the Garden State Parkway in New Jersey, which is fine for RVs.
I would take I-270 to I-70 to I-81, and then I-84 to I-90 to I-290 to I-495 to I-93 and from there whatever makes sense to get to what area around Lake Winnipesaukee you're going to. (Being one who doesn't like to pay tolls, I usually get off of I-93 at exit 10 and take route 3A north to just beyond I-89--or, more commonly, to I-89 since I'm more likely heading home to Vermont from somewhere in the vicinity of Boston if I'm on that bit of road. The Irving at exit 10 usually has fairly good prices for gasoline.)
Some here strongly recommend against I-290 due to congestion. I've never found it exceptionally bad, though I don't have a ton of experience with it.
Taking I-95 to I-287 to I-87 to I-84 (or something similar) is a good bit shorter, and probably often quicker, but I prefer to avoid going through the urban areas it goes through, particularly the Baltimore region, if possible. I would not even consider taking I-95 through New York City unless your destination was actually in New York City or otherwise required that route. That said, I have survived taking my motorhome to camp in Brooklyn a couple of times, so it's not an impossible task.
