We have just spent a week on Rhodes. We hired a car, picked up and dropped off at the airport (which saves transfers etc). There are several hire companies with the same terms, free second driver, included 100% damage waiver, no milage etc. We used George Rentals but as we had no problems I am unable to say what might have happened if we had. I suspect there would be no problem. Picked up car at 9.00pm (no paperwork, keys from kiosk) and dropped off at 9.00pm in the same way, took seconds. Many other firms do the same.
Its very cheap to hire a car and 100% worth it. Locals in Rhodes drive well (better than tourists on the whole). Note 50kph limits at junctions.
A cheap chinese ebay satnav (£45) with europe maps (usually included) is well worth it to get round Rhodes town and the first time from the airport (which may be at night). You can add (favourites) where you want to go using the map, as postcodes and road names may be scarce. I recommend a good map (B003ZIAZI6 use amazon) but get the hire company to add some of the new roads. Driving is easy, take it steady and note the speed limits (some are 30kph). It helps if you have a partner who reminds you "on the right", its easy to forget momentarily.
Parking in Rhodes town in Oct was tricky but plenty of places round the stadium, 1min to nearest gate, 5mins walk from the palace. You will get lost, the map [http://www.europetravel.gr/userfiles/image/Map%20of%20Medieval%20Rhodes%20Town.jpg] is pretty useful.
Food in Rhodes (I can't speak for Rhodes town) is variable and rarely the good old family greek cooking of yesteryear. Not a garlic or a charcoal grill in sight. I guess that's what most people want.
Supermarkets with good meat and veg etc are everywhere, some cheaper than others. Rhodes wine is cheap and OK (on the sweet side), and retsina always tastes better in greece (and is cheap and dry).