Using gustar to order food or drink.

In an early lesson, Amy used
“Me gustaría un café”
Why not “Mi gustaría un café” ?
 

Here is the grammatical explanation for this question.

present indicative: me gusta un café = a coffee is pleasing to me = I like a coffee

conditional tense: Me gustaría un café = a coffee would be pleasing to me = I would like a coffee

me = indirect object pronoun = to me
mi = my

The verb 'gustar' is a reverse construct verb where the object as we would think in English is actually the subject.  Here 'me' is used to specify to whom the coffee is pleasing.
 

Excellent explanation!

Thanks Robert
George