運動 usually means moving your body for mainly health or fun. So, I think it is right. I went to exercise ≒　私は運動に行きました。or 私は運動をしにいきました。 you can also ues エクササイズ instead of 　運動, it is more directly interpreted, I think. addition If subject of [ work out ]　is not human,　when [work out] means to go well, 運動 can not be used. technical: 運動 also be used for express moving itself. So, if you find 運動　in some scientific contexts, it often means just moving. e.g. 惑星の運動（moving of planets) 運動量（power of moving) etc.

yes it should say 'mainly for health'

Oh, by the way, about my English sentence above, is the location of mainlily correct? Shoud I move the word to between body and for?