I would go to Agra on Friday as soon as you arrive. It seems like it's a short distance, but it can take a long time. I'd also stay at the Oberoi. It's close and every room as a view of the Taj.
I'd skip Fatehpur Sikri and spend as much time at the Taj as possible. There is also another lesser visited site near the Taj is the baby Taj. It's a tomb across the river (I think) It's white marble and quite lovely.
I could spend an entire day at the Taj. It changes as the light changes. The inlays are gorgeous. I was so afraid my expectations were so high that I'd be disappointed. But I wasn't.
Have fun