Between Nydri and the next main tourism centre is the little port and beach of Mikros Gialos (small bay) that is a great little base for individual travellers for a day or three. The port village of Vasiliki on the southern underbelly of Lefkada is a haven for windsurfers: see this page or this one for more information. The little village is very pretty and is a good base for general holiday-making (as are the two other places). From Vasiliki there is a regular local ferry that runs to Fiskardo on Kefallonia (via Ithaca/Ithaki).
Crete, Santorini, and Naxos look quite doable within the 12-day block, but Crete’s beaches are scattered throughout a very LARGE island, Santorini really only has Kamari and Perissá (and some southern coast bays) and Naxos does have nice places to swim. If you choose only to visit those three islands in your relatively short time, you will do well.
For the full throttle, utterly extravagant Las Vegas experience, it has to be the Strip. You’ll stay in a grown-up wonderland, in opulent, palatial surroundings, and there is nowhere else on earth with nightlife and entertainment like this. Plus, when it gets too much, you can simply retreat to your suite within a few minutes. If you’d like to be close to the action, but without the full force of the Strip’s frenetic nature, stay East or West of the Strip. Here, you’ll find some smaller boutique and budget hotels, and you’re still in easy reach of all the main attractions.