I plan to spend my twenties and possibly my early thirties in a motor home and was wondering whether or not anyone knows of general areas in which one could park an RV without having to pay lot fees. I was thinking just general parking lots, however, there might not be anything but payed parking certain locations, so I was wondering about alternatives.

you could buy a membership to a recreational club & then you would have facilities you could park at long term.
General parking lots do not allow you to park RV — Walmart will let you park overnight for 1night. State Highway rest stops usually allow you to stay one night. If you are constantly on the move, that might work.

If you want long term parking, then you need to lease a space & hopefully one with electric hookup and sewer dump privileges. If you were or are with the military, they offer screaming deals and really nice RV parking sites with lots of amenities.