A "cool" store is Arrive on 17th at Collins. They have everything from limited Nikes to Cloak.
www.arrivemiami.com/ Eat at CheeseBurger Baby on Washington. One of the best burgers i've had and I've had a lot.
www.cheeseburgerbabyusa.com/ If you want to try "the best burger in the USA" as listed in GQ go up collins about 30 min to Hollywood, FL and go to a place called Le Tub. Go at lunch, the wait isnt as bad. It is huge (13 oz.) Its a dive but get a table on the water and watch the yachts go by. The waitress are 'characters' to put it nicely.
Also for some of the best sushi I've ever had forget Nobu and go to Shoji, Ocean and 1st. Make a res or go late.
www.shojisushi.com/ for some cheaper food I think same owner as Shoji try Big Pink in the same area (Collins and 5th maybe?) for sweet potato fries.
Cafeteria on Lincoln is good food too, open 24 hrs.
The Shore Club is a busy place at night, lots of gorgoeus women. Check it out.
Also, Pawn Shop is a cool club designed to look like a pawn shop.
www.thepawnshoplounge.com this is a little more 'hipster', shore club is a little more 'hollywood'
I assumed you were going to be in south beach... all of these place are there except for le tub and pawn shop (miami, not miami beach).
have fun, I love south beach.