I visited Japan solo for four days and found it very easy to get around, despite not speaking the language.
I'm a gay guy who sometimes travels solo. The UK is an easy destination, lots to do, and an easy jumping-off destination if you wanted to hit more of Europe. London - Paris - Berlin might be a fun itinerary. I would not do Iceland solo, just because I think the best way to see the country is to rent a car and we had to drive through some fairly gnarly storms while we were there (although it was December, so maybe you wouldn't have that issue). Reykjavik's one gay bar is hella cute, though. Australia, maybe? New Zealand is staggeringly beautiful, and if you've got an adventurous streak, the canyoneering is some of the most fun I've ever had. I visited Japan solo for four days and found it very easy to get around, despite not speaking the language. The gay bars I visited were smaller than my living room, and the patrons were politely confused by my presence. 10-15 days is a lot! Wherever you go, have a great trip.