Handgun, absolutely not while you live in Flordia. Handguns have to be transferred in the state of residence.
Long gun, possibly. Depends on the laws of your state of residence. Indiana it used to only be legal to buy a long gun in a neighboring state, but that law was removed a few years back and now you can buy a long gun in any state.
Long gun, handgun, or other? To my understanding, only long guns (rifles & shotguns) can be picked up at an out-of-state FFL.
Who's gun is it and who will be picking it up? Yours and you happen to be in the area? His as a gift and he will be picking it up? Yours, but you want him to pick it up since he is in the area?
From what I can tell and provided we are looking at a long gun, only the 3rd example would not be allowed. The second example may take some coordination with the shipper in order to make certain the firearm is addressed correctly when it arrives at the FFL. If you are planning on picking it up for yourself while you are here, I would check with the FFL first to make certain they are willing to do the transaction. As I understand it, not all FFLs are willing to do transactions for different states as they must comply with the laws of both states (i.e. an IN FFL would still be required to enforce IL's 24-hour waiting period for an individual from IL picking up a rifle in IN.)
To clarify ... I was wanting to buy a gun as a gift and have it shipped from an online ffl to another ffl...I would never touch the gun and of course I know an ffl would have it be used across state lines...its a lower receiver...but as stated I just bought him a gift card and he can get it himself