I'm looking for rental car prices - picking up in Nice and dropping off in Rome - to have the car for about 10 days. The big companies - National & Hertz - charge up to 800 euro for drop off in a different location. Does anyone have any suggestions on ways to avoid this fee or cheaper rental companies? Thanks for the advice!

Take the train to Ventimiglia and rent the car from there.

Michael has the best idea. You can either get a car from Ventimiglia at the very beginning driving it back to France and using it there as well, or get one car in Nice for the time you are in France, turn it in there, and then take the train to Ventimiglia to get another one to drop off in Rome.

Last month I rented a car in Germany from Budget and they did not charge a drop off fee. It's the reason I used them, they never do in the States either. It may be worth checking out
www.budget.com

The car was nice and the service was great.

I checked budget & they are sold out for all locations when I will be there! I will continue to search & look into Ventimiglia.