Well you guys are raising a very good point there, I can tell that having an accent does attrack people because they find you more interesting than, well accent-free persons.
Yet there are two sides to this. On the one hand people find you "interesting" but on the other hand people tend to not see you as the person you are but rather as the foreigner you are.
So what I'm trying to point out is that you'll always be in the situation of having to prove yourself in lots a situations throughout your day b/c you're the guy with the accent hence you're the foreign person.
So, as already stated, go spend time with native speakers, watch movies, work on your intonation and pronunciation, and study colloquial expressions...there's always time to impress people with your story once they figured you're from abroad