Directions to LIX. A video showing how to drive here.
For some hotel information in Orsay, in Palaiseau, and in Paris, see this page maintained by Catuscia Palamidessi.
If you are interested in renting an apartment (for a week, month, etc) near Polytechnique, my assistant has some suggestions and can help you find them. Science Accueil has as its primary focus the helping of visiting scientist to the Saclay - Orsay - Palaiseau area with finding accommodations. Some visitors have reported good experiences with the following two organizations that rent appartments in Paris: http://www.parisaddress.com/ and http://www.apartments-in-paris.com/.
Some advice recently offered (Sept 2009) for finding an apartment in Paris. The text is in Italian.