There is no airport ON Lefkas island. Nearest airport is located on mainland, 20-30 minutes drive away (I guess you know Lefkas is connected to mainland on a small bridge, so no need for a ferry or something). Airport is located near small town called Aktio, but for some reason it is named after the nearest larger town Preveza. So it is "Preveza airport" you have to look for rather than Lefkas airport.
It is true though, that I made a quick research in Olympic and Aegean airlines sites, and I couldn't find this destination either for some reason! I would wait it a few more days, then try again.
It is true that bus ride tfrom Athens to Lefkas and v.v. is a long one. It has been a few years since I did this, I think it was something like 6 hours. Ktel Lefkadas, the company running this route, uses some very new and comfortable coaches though, so although I suggest a flight if you can catch one, it is not the end of the world if you end up using a bus.
How long to stay on Lefkas it's up to you, your interests and your travelling style. There are some beaches that constantly get awards as best cliff side beach, best windsurfing beach and so on.... Porto Katsiki, Kathisma, Egremni and many more... There are many beaches mostly famous for windsurfing such as Vasiliki, Syvota and Agios Nikitas. There are busy resorts such as Nydri offering great boat trips to near by islands. There are inland traditional villages with great taverns, interesting churches and local produce such as Karia, there is a small waterfall (Vafkeri) ending on a small "pool" where you can take a swim ( not sure how much water will be there on June, still worths a visit). Lefkas is a lush island, so good for hikes on the shade too. It is an island that can serve as a base to explore near by islands and a part of mainland too. So how long to spend there, is really a personal call. I think a week is a good start : )
I am not familiar with Agios Nikitas accomondation.
Edited: 18 February 2011, 7:08