Today, LRO has published its first pictures. I actually got an official answer from NASA that LRO will take pictures of the Apollo landing sites. In fact, the answer was so friendly, I would like to post it here. Thanks to the people of Nasa answering questions from interested enthusiasts, I did not expect that.
This is the answer:
Thank you for your interest in the Lunar Reconnaissance Orbiter Mission. Nancy forwarded your email to me; I am the deputy project scientist. On board the spacecraft are the Lunar Reconnaissance Orbiter Cameras (LROC), in particular the Narrow Angle Camera, which will have a resolution of 50 cm from a 50 km orbit. This resolution is sufficient to image the Apollo landing sites. We hope to have good images of these sites however we may have to wait until lighting conditions are ideal in order to have the best images. Looking directly above a target, it is often the shadows that help one to distinguish features below so a low sun angle will give us the best images. All images will be put into the Planetary Data System within 6 months of obtaining them. The PDS is open to the public. However high value targets such as the Apollo missions will be released as soon as possible through an image-of-the-day on the NASA or LROC web sites or through a press release.
You might be interested in knowing that the public can suggest imaging targets through the web site put together by the LROC team. You can find it at http://target.lroc.asu.edu/output/lroc/lroc_page.html.
So if you think of a site that particularly interest you, be sure to submit it to the data base.