"What are you doing tomorrow night?" The use of the present perfect to refer to the future implies the idea of intent, and is much more typical. Also grammatically correct would be "What do you intend to do tomorrow night?" however, that would sound too formal for most situations.

"What do you intend to do tomorrow night?" sounds much more natural. You're asking about their current intentions for tomorrow night, not what their intentions will be tomorrow.

"What are you doing tomorrow night?" The use of the present perfect to refer to the future implies the idea of intent, and is much more typical. Also grammatically correct would be "What do you intend to do tomorrow night?" however, that would sound too formal for most situations.

This sentence sounds the best to me "What do you intend to do tomorrow night?" Providing you need or have to use the word "Intend" such as for a test or something. As a native speaker I would simply ask "What are you doing tomorrow night?" or "what are your plans for tomorrow night?". These are both more commonly used. Hope that helps :) Neil

Hmm... It sounds a little off. I think it should be "what are you intending on doing tomorrow night?" or "what do you intend to do tomorrow night?" or "what do you intend on doing tomorrow night?"