Louisville, KY to Bangor Maine

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).

I'm a "straight shot" kinda gal so I'd take I90 all the way. When you hit MA there are other slower, more scenic roots you can take to ME but if you want to stay on highway the whole time 90 will take you right to 495 or 95. You can take 90 straight to 495 to 95, cut off a corner by taking 290 through Worcester to 495 to 95 or go straight to 95. The stretch though the Worcester can be a little hairy at times but avoid rush hour and it's not too bad.

Living in NY, I'd agree 100% w/ DrewE and Crowe's posts. Like to add that PA tolls are very high from what I have heard. Think even higher than NY. Also, I 80 in PA, be careful/listen for accidents as they have quite a few and serious ones at that. NY can as well, but do have alt routes (5/20/17/86) if need be.