AP Style holds that you should capitalize “airport” when it part of a proper name. For example,
- We met at the Chicago Midway International Airport.
- How far does it take to get to Bradley International Airport?
The first name of an individual and the word “international” may be deleted from a formal airport name while the remainder is capitalized. For example,
- John F. Kennedy International Airport
- Kennedy International Airport
- Kennedy Airport
Use whichever of these are appropriate for your context.
Do not, however, make up names. For example, there is no “Boston Airport.” “The Boston airport” (lowercase “airport”) would be acceptable if for some reason the proper name, “Logan International Airport, were not used.