If you get to TJ fairly early, there won't be many people around. I'd advise staying away from places where you see lots of Americans, because that's where all the mugging will be happening -- like anywhere, tourists are easy targets. If you get a bit off the regular path and get into the downtown area, you can see some fabulous Art Deco architecture and experience some of the city's rich history. (Yes, my wife is an historian). Check out this article for a positive spin on what you might find:
http://travel2.nytimes.com/2006/08/2...?ex=1314158400