I know that both faire une promenade and se promener mean "to walk," but which one is considered better to use?
Promenade/promener do not quite equal "walk" (which would be the more generic marcher). They both imply a component of leisure, and are usually translated by "take a walk".
There is actually a nuance of meaning between se promener and faire une promenade, as the latter is a punctual action, but for the most part, both are grammatical. Personally I don't like faire une/des promenade(s) (I think it's clunky, especially in the plural), but it's probably just me.