Sharm el Sheik in Egypt might be OK the temps will be good, but you will need to be near Naama Bay if you want nightlife.

Otherwise Tenerife or Gran Canaria or Lanzarote.

The Caribbean is still warm then.
We stayed in Mexico (Riviera Maya) at the end of september/ beginning of October and the weather was lovely and warm. That is the tailend of the Hurricane season and so the start of their high season!
If you want nightlife etc., check the reviews for an island/hotel/resort combination that provides the entertainment or interests that you want. A good source of hotel photos and starting point for browsing is the Caribbean Warehouse site.
I am not sure but I think the site prices are for guidance and you have to phone for proper pricing, so if you do find something interesting, check around the web and TOs first to see what the going rate is!

caribbean is hot all year round.

I agree with chris sharm is the best bet because it will be hot hot hot and sunny everyday

We went to Crete last october 14 for a week and had excellent weather, Cyprus is nice that time of year as well.

We went to Cyprus a couple of years ago in mid October . The weather was perfect 25 - 30 degress in the day and lovely and cool at night , so you were able to sleep . Didn't see a cloud in the sky for 2 weeks!