"I am going back to the airport!"
Translation:Visszamegyek a repülőtérre!
Pretty much yes, -re (to), -en (on/at) and -ről (from) for repülőtér. This is also true for the root word tér ("square" in the sense of a broad open place) and other compound words that end in tér like csatatér (battlefield) or piactér (open air marketplace).
There are some cases where you might use the -hez / -nél / -től family of endings like if you're going to (the vicinity of) the airport but not really going to the airport proper. Both might be described as "to the airport" in English.