What's your definition of fine art? Are you looking for pieces by well-known artists or local artists? If there are pieces you like by unknowns there are deals to be had just about everywhere, including the US. And if you're looking for well-known artists, then a good art broker will likely help a lot in keeping you away from the frauds (Dali, for instance signed a lot of blank canvases).

I usually buy art when I travel, but knowing what you're looking for would help a lot in giving any suggestions.