I'm a travel agent and when I used to work for Thomsons they sent me on an educational. I went all around the island. Each resort is different. Obviously you have Faliraki for the 18-30's, Lindos and Pefkos are my favorites. After the educational I took my family to Pefkos. The best beaches are in the south of the island, plus its 10 degrees hotter down there. The island has a waterpark and Rhodes Town is great for a day out shopping (in particular the old town, which is beautiful).
Choose your resort carefully and you'll have a fab time.
It depends. If you want to go to party (Faliraki) or if your idea of a night out is a good meal and a few drinks at a bar afterwards (Pefkos...maybe Lindos).
I went a few years ago and had a great time (just the 2 of us!) and we hired a car to travel around the island for 2days as well. Rhodes town is a great day out on it's own.