“Did you go in to work today?”
You arrive home early from work, and your roommate is in the living room. Normally he gets home much later. You ask him if he stayed home today.
Did you go in to work today?
Use the phrase "go in" to talk about someone going to their workplace:
What time are you going in today?
However, you usually use "go in" only when you're not already in the workplace. When you're at work, you use "come in" or "get in":
She got in at 7 o'clock this morning.
You can come in a little later if you want.