There are three restaurants at Daytona Beach Airport.  MSE Branded Food Systems is in the terminal building and the other two (Cancun Lagoon Bar & Grill and The Olive Garden) are situated adjacent to the airport. You have to go outside the airport building, and the restaurants are on the same road (West International Speedway Blvd).  So if you want to eat at these two restaurants you will need to do so before you check in at the airport.

The details are as follows:

MSE Branded Food Systems which is on the main concourse of the airport
Telephone (386) 2399419

And two further restaurants adjacent to the terminal building on
West International Speedway Blvd:

Cancun Lagoon Bar and Grill serve a wide selection of grilled meats and fish, alcoholic and non alcoholic drinks. Take out is also available
Telephone (386) 2556500 or visit www.cancunlagoon.com

The Olive Garden serves a wide range of food including pastas, grilled meat and fish etc.
Alcoholic and non alcoholic drinks Take out is also available.
Telephone (386) 252 0639 or visit www.theolivegarden.com