Ixia nightlife is a bit low key really - Caballero Bar (close to Solemar) is popular and there is a couple of nightclubs at the far end (near the big hotels) but for a serious night out visit Rhodes Town.
Blue Lagoon is good for a cocktail/early drink - it's an open air sort of pirate/carribbean themed bar with pools, ship front, etc. It's next to a nightclub just back from Mandraki Harbour.
The best place to head though is Orfandinou Street. Get a taxi to drop you off near Alexia Hotel and you've got a full street of bars and clubs. You're bound to find somewhere you like there - there's Aussie Bars, Rock, RnB and so on...
You can find some pics/info on Blue Lagoon at
http://www.lepalais.gr