"Where do you go to work out?"
Native speaker here. 运动 itself is a noun. It means "sports" or "exercise" it can't be used in the same way as 锻炼 which is a verb "to exercise". You must use 做 with 运动 as in 你去哪里做运动？(which i tested is accepted) but you cannot use 运动 by itself. This is also explained by duolingo in the very chapter where 运动 is introduced.
I remember being frustrated with English when after getting used to a phrase 'I study AT school' I was sudden;y supposed to say 'I am going TO school'. In Russian we would use the same preposition in both cases, but English is different like that. So Chinese also has something different from English...