To travel within Europe you would need a Schengen visa. I could be wrong and I'm sure other members on here will correct me if I am, but I don't think you can get a Schengen visa while your still on a fiancee visa, I think you'll have to wait until you have got your 2 years FLR (Further Leave to Remain), which as someone else has just said could take up to 3 months.
I think that you could travel to other countries in Asia such as Thailand etc.
Iain.