It would really depend on what type of food you are looking for but I will try to help you out. For a special occasion I would try The Quarterdeck. They have great seafood. The Flying Bridge has alot of seafood but they also have pretty much anything else you could imagine. They also have beautiful views of the Harbor. If you want steaks go to The Coonamesset Inn. Have a great time!
Besides the good ones T mentioned (first answer) there are these.
Talk of the Town is supposed to be good but I haven't eaten here yet:
http://talkofthetownrestaurant.net/Home1...
Betsy's Diner on Main St. is great for breakfast, lunch, and dinner!
British Beer Co. is a good pub for lunch and is right across from the beach in Falmouth Heights:
http://www.britishbeer.com/local/falmout...
The Clam Shack at the end of the harbor is a very small take out seafood place and has the best fried clams you will ever eat! You can sit outside at tables (the roof is the best spot) and watch the boats while you eat, just watch out for the seagulls!
There is also a Hearth N'Kettle in Falmouth which is part of a chain of restaurants on Cape Cod that have good American food.