Europe is the place for you if you want to be upfront. Marriage probably doesn't matter, because if a country is progressive enough to recognize gay marriage, it's probably also progressive enough to recognize relationships without that piece of paper. In many places, such as Switzerland, the school will probably pay visa and transportation costs for your nonteaching spouse.

If you want to go to Asia or South America, the tourist visa route is probably the better one to take, then assess the situation when you get there. Just try to get a sense of whether or not you are permitted to have anyone of your choice in your accommodation--if you are not living on campus, that should generally be no problem.