There are a few carparks around - the most popular (and handy for the refreshments) is in the village of Newtown Linford. Go through the gates and along the road/path for a relatively short distance before the park opens out into a surprisingly non-Leicestershire type of landscape (it's not just 'up north' where you can climb to a hilltop and view a panorama of the nearby city)
The deer could be to your left in the woodland on the other side of the river (only a babbling brook really) or in the bracken-covered hillside to your left. The 'bellowing' deer in one of the above links walked out of the woods and into the bracken area and it was photographed on one of the many grassy pathways, so there are many chances of different types of shots depending on exactly where they are/lighting, etc.
This link has a zoomable map for access:
http://www.picturesofengland.com/England/Leicestershire/Leicester/Bradgate_Park/maps