Hello. Resorts on the east coast are best where it is less windy & where the best beaches are located.I suggest you look @ Lindos, Lardos & Pefkos.
On the Friends of Pefkos web site you will obtain more information.Free registration is required

I think Pefkos would suit you really well, lovely restaurants, couple of good cocktail bars ,2 good supermarkets, local bus service to Rhodes Town, lovely safe beach, no yobs and small but perfect as far as i am concerned.
I go every year and never tire of it even though it is quite a tiny village but it is safe and a good family place to be
Phyll

I love Lindos but would also recommend Pefkos if you're looking for a modern apartment complex. The larger apartment blocks in Lindos can get over run with wedding parties and being in a party mood they won't be in bed by 10pm and could easily disturb you.

if you're happy with basic studios and like the looks of Lindos then I would probably recommend the Avra. Right by the main beach so ideal for days on the beach and a very quiet spot at night.