There are a number of options in the area for landlocked fishermen. Surf fishing can yield decent catches of redfish, pompano, and the occasional shark or flounder. Many of the docks on the harbor have a lot black snapper on them, and some sheepshead as well. Before fishing on a dock make sure there isn't a 'no fishing' sign posted and make sure to be courteous and clean up after yourself.
If you are willing to get wet, wading the flats is a good way to catch speckled trout. You can also catch redfish, spanish mackerel, bluefish, and flounder around the grass beds.
If you are staying in Destin Half Hitch tackle is your best bet for bait. Live shrimp is probably the best 'go-to' bait. If you have a cast net you can catch your own bait on many of the grass beds.
check out the links in my signature for more fishing tips-while they are geared more towards boat fishermen many of the same techniques apply to fishing from shore.