The Island of Corfu. I'd already travelled a fair bit with my parents and we'd back-packed/island hopped around the Cyclades islands and down to Crete a couple of times. But when they suggested Corfu, even at 14 years old or so in the mid-70s, the images it conjured up were of mass tourism, crowded beaches, Brits eating Brit food and being "tyrpcal" Brits abroad. Really not my idea of fun at all. I preferred less developed places, sleeping out under the stars on beaches, or in a small tent in olive groves.
When we arrived on Corfu the first time we were back-packing. We went from the airport to the bus station which, back then, was down near the port. My old fella asked some European hippy types where we should head to. They pointed to a bus and said "Take that bus. Get off a place called Batos, and look for Spiro's taverna in the village. He has some basic rooms you can stay in".
We took their advice and found ourselves in one of those rare places, a low key gem, run by a lovely family and helped out by a Californian dude who helped make it a cool place for young wanderers to put down roots (playing great music in the bar and setting a very relaxed, welcoming tone). The nearest beach was like paradise, a walk though olive groves to a secluded cove, clothing optional, gorgeous sea, chilled vibe (no sunbeds or parasols) and a waterfall that cascaded onto the beach under which you could wash off salt and sand at he end of the day.
I'm still going back there every year now, some 46 years later. It's different, in many respects, but it is still paradise to me. I love the island as a whole, especially its green mountains and the wilder west coast (places like Lake Korission, full of flamingos and bordered by dunes full of sand lilies). And I absolutely love Kerkyra (Corfu old town) with its labrynth of alleyways and venetian architecture. But don't all of you go there, you'll hate it.
Another place has just come to mind. Malaga, the city. Absolutely superb. Cheap to get to. Loads of history, culture, beaches, great food, landscapes. Think Barcelona without the crowds.