The two places I most want to visit are the Andes and the Himalayas, for the local cultures and also mountains.
My favourite places I've visited (and the only, really), are Chamonix for the absolutely amazing views (there's nothing like having lunch in the snow at 3000 metres, looking out over the valley). A bit touristy and crowded, but the scenery and skiing make up for it.
London! I'm in love with it, it's like another world. Not only is it impressively huge with old, giant stone buildings and more modern architecture, it's full of so many different people from all over the world. Also has the best pubs and Camden Market.
The highlands! Clearly I have a thing for mountain ranges, but I think my favourite has to be in the highlands. They have a strange ability to be barren, lonely, eerie, and epic, but to feel like home at the same time. I went in easter, when it was still snowing but still possible to climb the mountains and ski, and although it's popular with tourists and people doing outdoor sports, it's still very easy to enjoy whole valleys, lakes, coastlines, etc on your own.