If you arrive middays in Agra, you shouldn't run directly to the Taj Mahal. The Taj is especially beautiful early in the morning. But there is something else you could do and shouldn't miss!
The Agra Fort lies also at the Yamuna River and offers some really nice gardens, nice buildings and a great view onto the Taj Mahal. There are many rooms to discover, even if most parts of the parts are closed for public.
The entrance gate "Amar Singh Pol" is already a small highlight as it's decorated nicely. Pass it and keep straight first and leave the buildings on the right hand side for later. You'll enter a very nice garden.
From there on just explore the buildings on your right and open one door after the other. You'll be amazed how many there are... I'm sure you'll find the inner court with a unique view onto the Taj Mahal.
I also made a picture of course and I later found out that at the same spot a picture was made for a guide book. Well, that should say enough about the view you can expect.
Entry to the fort is Rs.250 (plus levy = Rs. 500 per day)