Probably only accessible by bike or car, there is a place in the New Forest called Bolderwood that has a deer sanctuary which is home to quite a few fallow deer (Dama dama).
They regularly get fed which brings them very close to a viewing platform, although I was not there while that happened. A few stags are present in the herd and show off their magnificent antlers. The woods nearby are also filled with a lot of different woodland plants and the trees are full of all sorts of birds such as treecreepers (Certhia familiaris).
The grass is very long and when lying down the deer can be difficult to see with only a handful of antlers peering above the grass. One of the stags was a lot more fair in colour to the other stags so I was much more focused on getting great photos of him but he was very difficult to photograph due to his position in the grass and in the herd. Then when he stood up he was very focused on cleaning his private parts which made him look a lot less majestic.
There is a massive car park with a huge field, and a barbecue area within the trees. It is a perfect and cost free place to spend time with family.
However the busier times will lead to a more crowded viewing platform which could hinder shorter people and children to see the deer and in my case make it slightly harder to get good photos.
Address: Bolderwood Arboretum Ornamental Dr, Lyndhurst SO43 7GE