Love Charleston...
While never been fishing i can give rec on a lot of other stuff.
Dining you really cant go wrong with a little research. It is all about your palate and price point.
Hit up the historic district, Ft Sumter, take a walking tour, With your fishing and possible sullivans island trip it would be fantastic.
As for food....
Husk, FIG, 82 Queen, Charleston Grill, Obstinate Daughter, Hominy Grill are all solid choices.
We had a rec of Muse which we thought was great that many dont know about except locals.
You could eat five weekends in a row with numerous meals and if planned correctly never hit the same place and still have quality food.
Probably top 5 in US for food IMHO