I think this goes without saying but try to do things that you wouldn’t be able to do back home. Regardless of how stupid you might think you’ll look, the worst feeling would be to regret not taking advantage of the situation after the fact. I knew a person who finally got a chance to go to Paris and while there, didn’t go to the top of the Eiffel Tower because she was afraid of heights. Although the fear is valid, she regretted not going up for years, often bemoaning the fact that she made it all the way to Paris and didn’t go up.
This doesn’t have to be about extreme activities either. If you’re a foodie who wants to eat at a famous restaurant, go and eat there. Watch an opera at the Sydney Opera house. Try the waltz in Vienna. Enjoy the botanical gardens in Singapore. You might think going to some places are a bit of a trek but if it’s something you enjoy, by all means do it. It might be tough to get to, but the payoff is that much sweeter.