Just returned from the site (February 2013). It is not very wise to go there in winter (temperatures are currently around -16 C and it is extremely windy). But in spring, summer, or autumn it must be a lovely place.
To get there you need some preparation. I was advised to go to Doulun (direct bus from Liuliqiao Long Distance Bus Station in Beijing, 8 hours). In Doulun you should hire a taxi to take you to the spot but it is not easy. The roads are very bad and you will encounter some language problems. Xanadu (or Chinese Shang-du) is also a name of modern town which lies some 20 km from the site of Xanadu. Be sure that your driver knows where to go, otherwise he will probably drive you to Shang-du town.
There are no signs, marks of Xanadu (site) in neither of the 2 towns (Shang-du or Doulun). But once you get there everything is well described, prepared for visiting (signs in Chinese, English and Mongolian). The whole area is fenced and there is an entrance fee (but I was the only guest in February, so I paid nothing). It was not much left but at least you can see the walls, moats, ruins of temples and palaces, the roads, the layout is still visible. The whole area is surrounded by grasslands of Inner Mongolia