Don't bother with Lou's Police Supply, I used to be a frequent customer, now I won't go there at all. The one guy I liked there who was a quality guy and knew his stuff is now long gone. The rest of them are not very nice people, blatantly rude often, their inventory isn't that impressive, and their prices are high.
Security Arms near Pinecrest I can recommend. Their prices are a little high, but they make up for it with excellent customer service. They don't have much in stock, but are happy to special order stuff and are very fast about doing so.
Jet's Florida Outdoors is a good place. Still slightly high prices, but knowledgeable about hunting arms and some defensive arms. They're attitude is a little odd, but after a while I realized it wasn't that they're unkind, they're just very business-like.
Florida Armory I don't recommend. They're odd people (a little scary I found), and something about the whole place just smells of mall-ninja. Prices are also very high.
Miami Police Supply (not to be confused with Lous Police Supply) on either Tamiami Trail or Coral Way (I forget now), is an ok place. Average prices, not too high, not too low, but the guys are pretty nice. My only gripe with them is that they're not very safety minded and once took me into the staff room to demonstrate a firearm, loaded it, put a bullet proof vest on a chair, and shot it standing a few feet away with me a few feet away as well. If that doesn't bother you, that's fine. I haven't been back since then though. I only bought one gun from them and that was before that incident.
There is some other gun store the name of which eludes me not far from Lous Police Supply on 103rd. It's a pawn shop as well. Prices were sky-high and they were just rude. I never bought anything from them and never will. Also some of the phrases I overheard being used between customers and salespeople made me think of Liquor store robberies and crime. They also have a gun range I believe. Maybe I jumped to conclusions with them, but I'm just telling you what I personally think.
Aces Indoor Range and Pro Shop is ok. The guys are a little mall-ninja-ish, but the prices are alright and they seem to be nice enough guys. The manager seemed very friendly and knowledgeable. Maybe give it a look. Their range is ok too.
Big Als range and gun shop I think is technically in Miami-Dade. It's on Hallandale Blvd. on the South side which makes me think it's just barely in Miami-Dade. I wouldn't go there. The guys are weird, the prices and selection suck, the range is terrible (and I mean really really terrible), and I knew the owner "Big Al" (whether or not he's still the owner I don't know) through ham radio fests and clubs and he was an anti-semitic racist jerk.
If you're willing to drive north a little bit into Broward, I can highly recommend a few places.
IPS/911 Store is my all time favorite. Really nice guys, really great prices, and ok selection. They also have a training facility and range (frangible ammo only though). I've bought most of what I own now there.
Arizona Shooting range I don't personally like, but many seem to like it a lot. It's on 441 near Commercial Blvd. I believe. I've never bought anything there, mainly because of the prices. Very good selection though.
Only The Best Firearms & Accessories is significantly north of you. They're a neat shop though with NFA stuff and the only store I know of in South Florida that regularly stocks LMT AR uppers and lowers (lots of them) as well as plenty of AR accessories. Prices are somewhat high though. The guys are similar to the guys at Jet's Florida Outdoors in that they're very business like. It's not bad, just don't expect to go in there and shoot the breeze for an extended period of time.
Of course there is Outdoor World both near you and near me. The one at the Dolphin Mall I believe is now open. Haven't been inside, but I assume they have the same selection as the one up here.
Also up in Broward is Weston Arms. Average prices but nice guys. Bad ammo selection though (mostly Magtech ammo which is fine if that's what you like I guess). They just opened a new shop off of I-595 near University Drive. You could easily get to by taking the Palmetto Expressway to I-75 and then I-75 to I-595 and head East about 5-6 miles. It would be on the right side if you did that.
I think that sums up the ones I know of. If you have any questions PM me and I'd be happy to help.
ETA: Oh yeah, there's also Charlies Armory on Flagler St. East of the Palmetto expressway. Ok shop, nothing special. There is a gunsmith there. Also, I forgot that Florida Armory supposedly stocks LMT stuff too.
Also, as for Gunsmiths. I know that Charlie's Armory has one, Security Arms has one, and Only the Best has one. That's all I know about gunsmiths down here though.
If you tell us where in Miami you'll be moving to many of us could narrow down the list a bit.
ETA Again - I see you'll be in the Gables. That's where I used to live until I moved back up here.
You'll be very close to Security Arms in Pinecrest (very very close and I recommend you at least go in there and get to know them). Also you'll be close to Jet's Florida Outdoors, Florida Armory (don't bother IMO), and Miami Police Supply (maybe worth looking at if you're ok with a little bit of doofus-like unsafe handing, I wasn't but if you are take a look).