I've spent about half of my summers - or more - in Lefkada, the best beach in the entire world (and I've seen quite a few). It's beach town living - only about 25k live here - and it's another home for me in Greece. I've never had a bad day in Lefkada, and I'm being totally honest with that. It's also a bargain to go if you're into that kind of thing.
There's a nice monastery to visit; I think Greece has some of the most beautiful religious centres in general. It's more towards the centre part of the island and around the corner from one of my favourite tavernas. A lot of the island reminds me of my grandmother; even in her 90s, she'd stroll with me on the beach (as long as we spent an hour or more at the monastery) and we'd stay out until my tan turned into a burn.
If you have to visit any of the Greek islands I'll talk about, make this one your focus. There are shoreside servings; it's ridiculously cheap to go; and the people are incredible. It's the definition of getaway. It makes me feel like everything is possible.