Crete is beautiful, with lots to see and do - good sports opportunities - hiking, cycling, fishing, sailing etc. if you dont want to just beach it. If you're going in July, the main beaches and 'instagram' sights get heaving, so probably will want to hire a car and explore quieter areas if don't like crowds. Great weather and restaurants are relatively cheap.
Santorini is beautiful, but quite small and more expensive. I was there for a diving week, so can't comment on the culture.
Lefkada - not an island as such, as connected to mainland.. beautiful beaches and good for driving and exploring.. but we were there with family who had two crying babies, so if you're as intolerant as me, the holiday was destroyed... So I can't look back and remember much else..
Samos - not sure if many Brits go there - was surprisingly good, but a little less typical Greek due to its location - good food, quieter beaches and some very pretty fishing villages with good restaurants. Very cheap, baking hot, ****loads of vineyards and wine (stopped at a random one where the owner only spoke Greek and Russian and took it upon himself to make us dinner and insist we try all his wine types and homemade spirits) and also you can put your wife/husband on a ferry to Turkey shopping for the day and kick back, smoke a cigar in a deckchair, relax, watch attractive German lesbians walking past and enjoy the peace.
So to conclude... Can't go wrong with a Greek island ;