I'll second everything Sandy said and add a few points. We made the trip from Hudson, FL up through Apalachicola to Mobile Bay last year.
Apalachicola is a great town and I'd recommend spending a day or two there. If you decide to sail out of Apalachicola, you'll need to go south out of Government Cut and then west around the barrier islands up to Port St Joe.
Up the ICW (which I think is the better route), you can tie up overnight at White City if you like - just south of the canal over to Port St Joe. You can go west thru the canal to Port St Joe for access to the Gulf, or continue north in the ICW up to Panama City. There can be good anchorage across from the Panama City Docks, or out at Shell Island (the barrier island at the Gulf).
If you go outside from Panama City, the next tops are either Destin (8-10 hours) or Panama City (another 6-8 hours on). Inside, you'll continue from Panama City thorugh St Andrew's Bay back into the ICW, then out into Choctahachee Bay to Destin/Fort Walton Beach.
From Destin, you can go outside or inside to Pensacola. Very nice sailing through Santa Rosa Sound if the winds are right. There is a pretty anchorage at Fort McCrae, just to the west of the entrance to the ICW on the west side of Pensacola Pass.
If you go outside from Pensacola, the next stop is Mobile Bay. There are a lot of oil rigs offshore through this section.
Inside from Pensacola, you'll go through Big Lagoon, and there are several good diversions. First, you can go up into Perdido Bay - generally, stay south of the US 98 bridge, and there is good anchorage at Tarklin Bay on the eastern shore.
Just west of Perdido Bay, you'll find Pirates Cove, which as Sandy says is worth a stop - anchorage either out front, or behind in the cove. With a smaller boat you can get right up on the beach next to the restaurant.
Just west from Pirates Cove is a newer marina on the north shore, Barber's Marina, with full fuel service and pump-out but no restaurant. On the south shore is Bear Point Marina, full service and a restaurant.
Just west of Pirates Cove/Barbers is one of the prettiest anchorages on the ICW, Ingram Bayou. Turn north at bouy 72 and anchor either in the lower portion of the bayou, or just to the west after the bayou takes a hard turn to the west.
Continuing west, you'll first pass Wolf Bay to the north, somewhat shallow; then back into the ICW, LuLu's is a great restaurant and marina, just east of the Alabama 59 bridge.
As the ICW opens out into Mobile Bay, you can follow a side channel to the north and then east into the Bon Secour River - good deep channel, some fresh fish places along the north shore, and anchorage up the river at the last channel markers.
In Mobile Bay, on the east shore there's Fairhope - no anchorages, but a nice town and docks at the City Docks and in Fly Creek. On the west shore there's the Dog River, several good restaurants and anchorage about 2 miles or so west of the bridge; and the Fowl River, if you fit under the bridge (45' clearance) with anchorage across from Bellingrath Gardens - turn north where the river comes to a "T" and anchor across from Bellingrath's mansion and docks.
Down on the ICW across the Bay, there's a decent open anchorage at Navy Cove, and a good marina and restaurant (Tacky Jack's II) a couple of miles east of the mouth of the Bay. On the other side of the Bay, there's a good anchorage at Sand Island, on the Gulf side of Dauphin Island in front of the Dauphin Island Golf Course.
In Mississippi Sound there are anchorages on the north shores of Pettit Bois, Horn and Ship Islands - good if the winds are out of the southern quadrants, but if out of the north they'll push you up on the beach. There's a small island up near Pascagoula that you can hid behind in north winds. Stay in the marked ICW west of the Dauphin Island Bridge until you reach the west end of Dauphin Island, it shoals rapidly north and south of the marked channel.
Ocean Springs, Biloxi and Gulfport are on our list of cruising locations for this year, we haven't been that far west yet.
This is all just an overview, if you want more details please let me know - either post a reply or send me an PM here, I can give you some details of marinas we stayed at between Apalachicola and Mobile Bay.
Mike Turner
Lazyjack 32 schooner "Mary'Lis"
Mobile Bay, Alabama