Good choice Herbie - I love Lanzarote for a winter break, but Rhodes beats everywhere I've been as a beautiful island.
Be sure to check out Lindos on the south west side of the island - 2 beautiful beaches, and no cars are allowed in the town (and they wouldn't fit anyway as it's all wee twisty streets). Check out the castle and old town in Rhodes town too.
They local bus service is good and you can easily get from one end of the island to the other.
I've never been to Faliraki, but I'd probably skip that!