Walking distance to Rhodes town from Ixia is about 2-3 miles

My parents would often walk from the Atlantica Princess which is pretty much in the centre of Ixia, that would take around 1 and 1/2 hours to the harbour. The walk is quite a bit shorter from the bigger hotels near the traffic lights - Cosmopolitan, Dionysos, Capsis.

Yes your teens will be able to get to Faliraki and back easily by taxi (though i'm not sure of the current fare) but if it's nightlife they're looking for they might be just as happy in Rhodes Town. If they head for Orfandinou St, that's the main bar street in town.

Have a look at http://www.theixiangrand.gr/ for a decent hotel in Ixia. A walk towards Rhodes from ther will be a good hike, but if you walk to the end of the shopping parade on the main road, then get a bus in to the centre for 70 cents, you'll see a lot more of the place. You won't be as hot either.