We've been going to Marco Island for the holidays for the last ~10 years. I pretty much agree with most of the suggestions here, but would add a few more:
Speakeasy -- Good pizza and Italian dishes in a fun atmosphere. Thursday(?) nights they have karaoke with some pretty good singers most of the time.
Marco Island Brewery -- Large menu, decent food, great beer selection in a large sports bar atmosphere. Always a fun time there, and a great place to spend an afternoon watching a game.
Cocomo's Grill -- Home of the famous fried hogfish. Good seafood selections, and the best place to take your fresh catch if you were out fishing earlier that day. Their Cocomo Bread appetizer is to die for.
Little Bar Restaurant -- Venture out of the main Marco Island area to Goodland, and you will find this gem. Casual, old school place right on the water with an old Florida feel. Food is always good, and if you are there during stone crab season, this is the absolute best place to experience them!
Capri Fish House -- Technically off the island, but only about 15 min drive to Capri Island. Dining in an open-air grass thatch hut literally 10 feet from waves lapping on the shoreline makes for a great dining experience. Large selection of seafood dishes is their specialty. Always a special night out there.
It was mentioned in Doug's video, but another vote for Joey's Pizza, which I think has the best pizza on the island.
And another vote for Pinchers; even though it is a chain, they have consistently good food there at reasonable prices.
Kurt