"Mis padres fueron a dejar a mi tío al aeropuerto."
Traducción:My parents went to leave my uncle at the airport.
Están aprendiendo español, como yo. Estoy de acuerdo que las discusiones debería ser en español.
Aunque fueron a dejar = went to leave, esta oración es un poco raro en inglés. "Leave him at the airport" significa (insinua?) que no les gusta el tio y nunca quieren verlo.
Es mejor de traducer la oración en una manera menos literal.
take = llevar
drop off = dejar
My parents went to take my uncle to the airport.
My parents went to drop my uncle off at the airport
First of all, no English speaker would ever say this. It sounds like they are abandoning the uncle ("My parents went to leave my uncle at the airport. We never liked him anyway"). Instead we would say, "My parents went to take my uncle to the airport."
That being said, in English, we take things "to" places and leave things "at" places (or "on" things). For example, "My parents left me at home, and went to take my uncle to the airport." "I took my car to the mechanic." "I left my keys on my desk."
As far as your examples, Roger would hail a taxi and tell the driver, "Take me to the airport, please." Once there Roger might say, "Please drop me off by the passenger information booth."