I’m actually about 45 miles west of there, and haven’t road tripped that far east in a while.
Silver Sands Outlet Mall- not always the best prices on everything, but if you poke around, there is good stuff at very good prices. Take US 98 east towards Destin for something like 45 minutes. It’s just past the big Sandestin Resort complex on the north side of the road. My favorite places there-Westpoint for linens, the Saucony store for its $10-$15 sample sale rack, Polo, J Crew and Banana Republic for clothes. There’s a really really good pizza place called Ciao Bella in the western part of the mall, and the gelato place gets a thumbs up as well. There are a couple of shopping areas in the Sandestin Resort (Market Shops at Sandestin, Village of Baytowne Wharf) that offer higher end clothing and such, but you will pay full metal retail price.
Bass Pro Shops- interesting for it’s giant aquarium (see what you’re going to be swimming in the Gulf with) and lots of different fishing and hunting gear but I find it overstimulating. Should be a source of decently priced CO2 cartridges, but I haven’t priced them there yet. Also on US 98 about 10 miles west of the outlet mall. A bunch of other stores in the same development (Destin Commons) are scheduled to open some time in November.
Seaside- cute to the point of twee beach town that was the set for the movie The Truman Show. Take US 98 west across the Walton County line, go left (south) on CR 30-A for a while. Good bookstore, interesting, but spendy stores. Similar smaller cute little beach developments with shopping areas- Carillon Beach at US 98 right by the Bay County/Walton County line, Rosemary Beach on 30-A before you get to Seaside.
Alvin’s Island- the ever present t-shirt store chain. There’s a big one somewhere on the main PCB road that has a live gator enclosure that’s kind of neat. Ask directions from whoever you’re staying with. They’ll know what you’re talking about.
There’s a big new shopping center (The Pier Park development) in the planning in PCB, that is eventually going to be pretty cool, but it’s probably a couple years before completion. The Panama City mall is a generic mid-sized mall with the same stores you get at every other mid-sized mall in the US.
For general food, the good grocery store chain is Publix. Very reasonable prices for Gatorade and Clif Bars, their deli subs are good when you want a quick no-fuss meal, and they’re a major sponsor for one of the big tri series in Florida (Publix Family Weekends)