I left my honeymoon in the hands of my father (mum and dad were paying as our wedding present) and we ended up in Davos, in Switzerland, a ski resort in the height of summer (end of july / start of august) which was a bit odd in that I'm used to places closing for the winter, not the summer but it was enjoyable, we did plenty of walking and exploring the place, including attempting to swim in the lake, which turned out to be a lake that fills up with glacier melt so is always freezing!
A cheap sunny, lay on the beach but able to explore holiday? I'd got to Soller or Port de Soller in mallorca, It's a small town at the quieter end of the island with a beautiful beach where you can enjoy the sun, the bars and swim, but also you can happily go off for a wander around the area or drive to the more touristy areas.
my in-laws own a small single apartment set in a small orchard (so on it's own, not part of a block of apartments) that they rent out, if you want details, message me and I'll get the details for your. It's a short walk down to the beach, the trams stop right outside if you didn't want to walk back.
Although if we include the honeymoon, that might be harder. But if we don't call it a honeymoon, just a conveniently timed holiday....
