OP, here's a few to explore if you want to stay in O town.
Buffalo Bills On Mills Ave is in Downtown Orlando, small shop specializing in Muzzleloading, they have a few modern guns and general stuff. Good folks, solid reputation.
Southern Oaks is on south Orange Avenue, not far from Downtown. Haven't been there in years, don't know what they have.
Riegs Gun shop and Range on South Orange Blossom Trail. Again, haven't been in years, couldn't say how they are now.
Replay Gun & Pawn on East Hwy 50 is close to UCF, I was in there a couple years back, they had a decent inventory and a working gun smith in the shop.
And Bass Pro on International Drive.
If you have a car and want to make it a day trip, there are sights to see away from Orlando.
Gander Mountain in Lake Mary is 30 minutes east on I-4, the bill themselves as Florida's Largest Gun shop, and they have a very nice Range.
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Everything there is ridiculously over priced.
In Apopka, as mentioned, Spikes, and Shoot Straight, not to far apart.
A little down the road from Shoot Straight, in Mount Dora/Tavares, is Petersons Gun shop, which may be the oldest gunshop in the Country, it was moved here from Cody Wyoming in the 60's, lock stock and barrel. Axel Peterson hand made rifles for the likes of Wild Bill Hickok and his Contemporaries. Much of the old gunsmithing equipment and some of the original guns are there in the original shop.
The rest of the place is an old time Family run Gunshop. Good people.
In Deland, cruise 17-92 from Orange City, half a dozen Good shops on that run, AAA Gun &Pawn is the only gun shop in Central Florida you really need to see. Takes an hour just to work around the perimeter. Every Gun you can dream of, floor to ceiling, ceiling covered, walls covered, stacked 20 deep in the corners. ARs to Mausers, Levers, bolts, FALs, you name it, they have it. Every imaginable pistol in cases on all four walls.
Do not stop there if you are a fan of 1911s, you may never come out.
Further down the road, in the Deland Airport Industrial center, Tactical Machining has their manufacturing facility, CNCing AR parts, they used to sell blems and lowers out of the front office. Haven't been by in a couple years, so I can't say if they still do.
There's more, but that ought to keep you busy...