I know that both faire une promenade and se promener mean "to walk," but which one is considered better to use?
If you say "je vais me promener" without saying where, you're going to wander, hang around.
But if you say "on va se promener en ville" ou bien "on a fait une promenade en forêt", you mean a real walk, enjoy the landscape, whatever.
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.