My visit to Battir took place in June 2013. At that time, the boundaries of site were unclear. (now available at http://www.bic.com.ps/bcc/images/BaNF%20Final.pdf). So I went around a bit by chance.
I took bus 21 from Jerusalem to Bethlehem (Bet Jala). A first glimpse at the site happens right after the two tunnels under Bet Jala. There, on the right of the road, lies the main core zone, with a very nice valley bordered with terraces and olive trees. A better glimpse appears as the bus turns back toward Bethlehem.
After leaving the bus, I hired a taxi to get to Battir. It is a 10 minutes drive.
There is a also a bus from Bethlehem, leaving from Cinema Plaza, to the village of Battir.
At the center of Battir village lies the the Ain Al-Balad source. It was a very warm day, and children and teenagers were playing in the water. It is part of the core area, the village itself being in the buffer zone.
Below the source lies the ancient roman pool. From there, several hiking path lead to the westren part of the core area (I lacked time to hike there).
After the village, the road continues into the eastern valley, with plenty of very nice views on the agricultural terraces made of dry stones and the olive trees.
Battir is an pleasant and easy side trip from Bethlehem. You can spend an hour (like I did) but also hike around for a full day.