I am not a teacher.
"A and B alike are both good choices." sounds like overkill to me.
"Both" is good, it's "alike" that doesn't work.
I think you mean, "A and B are both good choices." or, " "A and B are equally good choices."
To use "alike" adverbially you would have to turn the sentence around to something clumsy like, "The [quality of being a good choice] applied to A and B alike."