Is it ok to say "I'm staying up late tonight because I'm going to the party"?
Is the phrase "stay up late" used only when you're doing something at home?

Question

Answer

The sentence is grammatically correct.
Staying up late just means to sleep very late, no matter where you are.

Answer

Staying up can be used whether you're at home or outside. It just refers to being awake.

Answer

No it is not. Example:  I am staying up late to go to the party. The doors only open at midnight.