I've been to Lefkada island several times and I've experienced many of the islands fun things to do. With a nice stay of lets say 5 nights you can experience everything in the list below and maybe even have some free time to actually lie on the beach for a little while.
Visit the very famous beaches - Lefkada island has some beaches which names are spread all over the world and tourists from all around come to visit them. One of those bitches is, of course, Porto Katsiki, but there are also many others that deserve to be mentioned in our list, that's why we have a separate post just for them, The top 5 beaches of Lefkada in the Greek Ionian Sea.
Nydri water falls - very close to the city of Nydri, hidden in the forest, just within a half an hour walk, or maybe even less are the waterfalls of Nydri. It's a perfect place to visit and have some exercise, justa make sure to bring some trainers an sports clothes, it's not impossible to go even with flip flops, but I think you'll be much more comfortable with something on your feet. I don't have unfortunately a high quiality photo of the waterfalls, but you can always check them online at google.com.
Paragliding over Kathisma beach- yes, you read that right, paragliding! Situated high in the mountains on the west shore of the island, a thrilling adventure awaits you to fly over the island and enjoy the great views and turquoise blue waters of the Ionian sea. The meeting point for that event is at Kathisma beach, they'll take you the highest point and from there you'll paraglinde with a guide back to the beach. The price was 80 euro and the duration of the paraglide was 20 minutes, but the overall duration of this activity was about 1 hour, to get from the beach to the mountain and get equipt before the glide.
Sail around the island - is one of the things that is a must do on any Greek island. That's the best way you can reach some of the beaches, actually not any, but in most of the cases the best ones, like Egremni which was also accessible by car and few hundred steps, but an earthquake in 2015 made it possible to access only by boat by destroying parts of the road and all the stairs. Also, if you have the opportunity to spend more time on a aboat and even better, hire a private one just for you and your friends, if you're traveling with some, that is, you can even go to the near by islands, and from Lefkada there are many you can visit, like Paxos and Antipaxos, Kefalonia, Ithaca, no a little further away are Corfu on the north and Zakynthos on the south.
Eat Greek food with an outstanding panoramic view and sunset at Rachi restaurant - one of the most incredible experiences in Lefkada island, have dinner while enjoying the sunset. The restaurant is located high in the mountains, it's the point where the paraglinding starts and since it's located on the west shore you get the see an amazing sunset on a clear day, not to mention that the food was delicious!
The water sports at Vasiliki - I small bay situated on the south side of the island, that offers water ski, parasailing few other fun activities and a couch if don't know any of those but want to learn. There is also a scuba diving and of course boat renting, it may be the closest location for such services. Other than that the bay is very beautiful and you can just and have lunch, bon appetite.