If you are looking for casual - some of the best sandwiches and salads can be found at Stack's Coastal Kitchen in Mt Pleasant, near the Ben Sawyer Bridge on Hwy 17 in a Bi-Lo shopping center. They do a lot of take out but have 7 or 8 tables to eat in. Mostly a lunch place. Everything is made from scratch, and delicious. Perfect take out for a trip to nearby Sullivan's Island. Yum.
For dinner and a bit fancier than Stack's, Graze which went in the old Coco's Cafe space (by Mt Pleasant Whole Foods) is quite good and has a great happy hour for drinks and small plates. Also Eurasia in same shopping center is nice but slightly pricier than Graze.