Pardon me for saying so, but this is bad advise. Just a few years ago Miami was well known for tourist muggings and car jack attempts. The signs from the airports directing tourists to the usual destinations have improved, but not much else. Like any large city, one wrong turn can place you in a bad situation. There are many bad areas that must be avoided. If you don't know your way around leave the expensive stuff at home.
OP:
As for shopping for watches, Miami does not offer much in the way of vintage. There are some nice shops downtown where you can find previously owned luxury watches. This area is pretty safe during the day, but stay away at night.
For a nice stroll South Beach is pretty popular. Start on Ocean Drive and 5th, and work your way North. There are restaurants, clubs, hotels, art deco architecture, and the beach to keep you entertained. Be prepared to pay ridiculous tourist prices here and at the nearby trendy Lincoln Road Mall, an outdoor area that is also good for a nice stroll.
There are many very good upscale restaurants in Miami. Too many to mention. However, to me Miami means Cuban food. Best in the world. If you venture to SW 8th Street and 35th Avenue you will find Versailles Restaurant. This place offers some of the best Cuban food in the world for very reasonable prices. It isn't fancy, but it is the real thing.
Have fun.
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