All of the deers around the Park or the Temple grounds roam free.
The biggest attraction is 1) Feeding the deers (~150 yen biscuits/ deer "Senbeis") and 2) Todaiji Temple (The Great Eastern Temple).
To get to the Park and Temple, take the Kintetsu Nara Line Rapid Express and get off at the Kinetsunara stop. Then just follow the signs towards the very end(all in english ^^). You will reach the Park in about 5-10 mins and 30 mins at the temple. You can buy a combo admission of the Buddha Hall with pass for the Todaiji Museum (800 yen; but unfortunately it seemed like the museum was closed when we were there).
Tip: Watch out for deers with horns! They may look tame and cute, but once they spot you with biscuits in hand, they will chase you like there's no tomorrow (see the 1st picture--no that is not me). I was unlucky and was attacked by one as I tried to feed it, but another deer kept snatching theirs before they could get to it so it got angry with me. Another deer bite my significant other.
Daibutsuden Hall: 7:30a- 5:30 (April to Sept.; everyday) Admission: 500 yen
Vendors: You can buy all sorts of cute deer-theme things on the
perimeters of the temple and along the walkway (mom and pop shops). I found
cute hand puppets, Snoopy, Hello Kitty, and Rilakkuma deer merchandise.
We also witness the Park rangers carrying a deer away on a stretcher...not sure what happened. Sorry no picture, but it was kind of epic.