I'd probably either take I-80/I-84 or go up to I-86/I-88 across the southern part of New York state. It's nearly impossible, or at least rather impractical, to avoid all tolls on this trip if you're sticking to expressways. If you have the time, you can take various secondary roads instead, such as NY7 to VT/NH 9 rather than I-90 across Massachusetts, or maybe heading up to US2 and then east, etc.
I-90 is the New York Thruway, and is a long stretch of toll road (and the tolls add up to a substantial sum by the time you get across). I-76 is the Pennsylvania Turnpike, and similarly rather spendy.
Be aware that the Google map directions have you going on routes that are not permitted for RVs on its the southern route option. Any "parkway" in New York and Connecticut, with only one or two minor exceptions that don't apply here at all, is restricted. (The Garden State Parkway in New Jersey is okay for RVs, but it's also not on the way for this trip.) It looks like it also has you going through NYC a little, which is not my idea of pleasant driving (and perhaps even less fun once you adjust it to avoid parkways).
