"Where do you go to work out?"
So... why can't it be "you go work out/exercise where" like almost all of the sentences I have been seeing?
"你去锻炼哪儿?" Why would this be wrong?
Place must go right before the main verb. The question word "where" (哪儿) is the place. "Work out" (锻炼) is the main verb.
Yes, "... go to exercise." would be proper, and should be accepted.
Another way to look at it is that place (哪儿/where) must go right before the main verb. The main verb is 锻炼, not 去.
I'm not a native Chinese speaker, but I don't think you can say 哪儿去，at least not in a context such as this. It's 去哪儿. The location (in this case, "where"/"哪儿") has to come after 去.