I wouldn't stay in Nadi if I were you. It's a nice enough town but not the Fiji you might dream of. You want to be on the beach - get out to one of the islands! There are two types of night life in Fiji. One is western style (although, like the other reply says) it is comparatively tame. For that some of the resorts on the Yasawas/Mamanucas, could be the answer - beachcomber, teh resort etc. But there is also the Fiji-style night life - kava drinking. Fijians, mostly men although that is changing slowly, stay up all night drinking, talking, playing music and singing. It's wonderful but it can be hard to get invited as a tourist. Either you stumble into it by luck or I know that Vorovoro Island is big on kava drinking (www.tribewanted.com), although I'm not sure of it is possible to stay there for only 3 days - might be worth asking. I can't think of anything else off the top of my head.
Enjoy your birthdays!