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We went to Fuerteventura a few years ago. Stayed in Caletta de Fuste (now Costa Caletta), we visited Jandia and Corralejo and none of them were 'drunken brits abroad' type places. It was a few years ago though, may have changed. TBH I preferred Jandia as a resort, lovely beaches, Caletta was nice but the beach wasn't brilliant (IMO), I liked Corralejo too.
Cyprus is nice if you avoid Aghia Napa in season. Coral Bay, near Paphos, is my favourite resort, a nice quiet resort but with shops and restuarants/take-aways. It caters mostly for villa holidays (package and independent). Larnaca/Limassol are the best bases for exploring the island.
Could the Dalmatian coast of Croatia work? Miles and miles of beautiful, clean beaches, and some interesting sights. We mostly self-catered (we were there pre-kids and could roam around) but the two package hotels we stayed at were quite peaceful, and it's not too expensive to get to either.
We're planning our first 'beach' holiday with the kids (3.5 yo twins). Before the kids came along we did walking/sightseeing holidays (eg. Austria, Lake Garda, Iceland etc), but I think now we need something more child friendly. The kids will be happy with a pool with a slide, and a beach, but looking at family resorts on Tripadvisor I'm worried it's going to be noisy and I'll end up hating it.
Help, has anyone done a package holiday that wasn't too expensive, but not full of the cliched drunk Brits abroad? Or am I better off sorting it out myself so I can choose a quieter location?