Honeymoon suggestions for artists

Hi all! Hope this is okay to post! My partner and I are looking into having a honeymoon, but we're in real need of some suggestions for a spot. A little about us:

• We're living in the UK. I'm from Bulgaria. We'd be flying from London.
• We'd like the honeymoon to be in a place that's not in Europe – we often travel to and from Bulgaria, and in a way Europe seems… Well, close and easily accessible at the moment. We want a place that will be almost a one in a lifetime, something you won't be able to do as easy with a kid let's say.
• We're not big on staying in fanciest hotels / all inclusive spots, we don't like visiting a place and just staying at the hotel/resort, doing nothing but lounging around the pool etc. We're not adrenaline people either, no bungee jumping or shark swimming etc. We're somewhere in the middle. On previous trips we've taken plenty of enjoyment just walking around a new town, getting lost, having a cup in a small shop, visiting a local museum or finding a lovely park to have lunch at.
• We're both artists, in our twenties.
• He likes snow and forests, I like summer and the beach so that's our only real difference.
• Our budget is around £5k
• We've been to Germany, France, Denmark, Italy and Portugal.

Hope this is enough, any recommendations are good recommendations! Xx