Here are a couple,
Florida Gun Center
Ace's Indoor
Stone Heart
Nexus in Broward, Ft Lauderdale/Davie area as mentioned above
Pembroke Range as mentioned above
I know that Ace's Indoor will rent guns to nonresidents. They get a fair number of tourists there. I would assume the others do as well, but probably worth a phone call to verify.
On the reviews, Ace's has had some bad reviews and in the past it was a deserved bad reputation, but it's turned around for the better. OP, if you want to ask me any questions about Ace's about it, feel free. I go there about 3 times a month. One thing, coming in, renting a gun, buying the ammo there (you must with the rentals), range fees, more ammo, etc it can add up quick.
Depending on when your friend will be in Miami, I may be able to meet them at Ace's or Florida Gun Center, and bring a toy or two.