Based on a bit of internet research, apparently, both options are correct.
But seems like most native English speakers will go with "What time", which to me sounds kind of incomplete.
And not trying to stir the pot even more, but in the comments section of the second link there's even a guy saying that certain uses of "at" sound ghetto... Is that true?
Peron 1: is it acceptable to say "this is where it's at" when reading a map in search of a specific location.
Person 2: No!! The whord WHERE took care of it, using the word at in this instance is a run on and repetitive!! Ex: Where ( Location ) you at?? Sounds very ghetto and is dreadfully grammatically incorrect!!
I know that's probably a much worst usage of "at" than what I'm mentioning in the title, but is the "at" in "At what time" redundant? Does it sound that bad? Would you right away say; "not a native Engish speaker".
The thing is, as a native Spanish speaker, we'll say "A que hora" == "At what time", if we remove the "A" which would be like the "At" it just doesn't make sense anymore ("que hora"), so to me it feels much more natural to say "At what time". But I don't want to sound like the grammatically correct guy that sounds weird at the same time.