뭐 하고 싶어요? sounds more natural.

thanks!

뭐하고싶어요? = what do you want to do? Ex)Q. 저녁먹고 뭐할래요? What do you want to do after dinner A. 영화는 어떠세요? How about watching a movie? 무엇을하고 싶어요?=Which do you want to do? Ex) Q.밥 먹고 영화보거나 카페가는것중에 뭘 하실래요? After dinner, Which do you want to watch a movie or go to cafe A. 영화보는게 낫겠네요 I think watching a movie is better. 무엇을 할래요 -> 뭐 할래요? Is better. Not using that sentence in korea :) 뭐 하고싶어요 -> it's correct expression. Ex) 카페 들렸다 뭐 하고싶으세요? Cheers mate ;)