I've been lucky enough to visit Mauritius quite a few times now so could give you a few ideas on what I think...
For nightlife, the North of the Island (Grand Bay) is probably the most 'happening'. It's definantely a draw for tourists, and there are lots of small bars and some nightclubs too.
I would certainly recommend the banana cafe here- a both chilled-out and lively bar located opposite opposite the beach. It plays music until late and has a a very tropical feel, with a sandy floor and is partly open-air. There is a club right nextdoor called Zanzibar which is pretty cool but quite small or just a walk along the the road there is a bigger club- Stardance it's a more commercial club- but still worth a try...there are some really cool clubs dotted around the island, but these are a little harder to find, unless you're with someone who knows! I would stick to the north for nightlife, but also try Port Louis in the evening- the big complex 'Le Caudan' has some nice places too!
As for beaches- hey, you're in Mauritius- it doesn't really get much better! If you stay in one of the big hotels, they usually have beautiful private beaches, but I would highly recommend getting out and about to discover the real Mauritius for yourself.
Again, the North has some beautiful places, try Toux aux Biches for a gorgeous beach with lots of watersports, and if you want a long walk along the beach to Pereybere- you'll find a busy but lovely beach and shops. West of the island is Flic en Flac- which in my opinion, really is a beautiful beach- and huge! Another one to try is Le Morne (South-West), which is a stunning and vast beach near some of the really prestige hotels, and is overlooked by Le Morne mountain.
The windiest part of the island- I'm not too sure
A place called Gris Gris in the south of Mauritius is known for being windy with rough, dangerous waters- so I would guess that it's proably windiest here?
Depending when you visit Mauritius (hottest time starts in October)- it's definately hottest in the North so make sure you take your suncream!
Anyway- hope this is of some help- have a fantastic time- you will anyway...the place is beautiful, the food is wonderful and the people are warm and welcoming- ENJOY