The first one is exactly correct: 你今天会做什么=What will you do today The second one "你今天在做什么" is not a clear question which we might not ask in order to knowing others' plans for the day. Reason: "在做" = be+doing, so 你今天在做什么 is more or less like "What have you done/been doing today"，but actually people do many things in a day, so need to make sure the situation before you use the second one.

Not sure if its right haha since I'm also learning, but I think the second one sound more correct. Usually I use when chatting with friends I use: 你今天干嘛呢？

或许我们可以互相学习……