Now that Philae has woken, is more known about its exact location? In other words: does Philae know where Philae is?
Navigation on Churi sounds challenging.
Yes, the science/engineering teams will be able to use the radio communications between Rosetta and Philae to better pinpoint the location of the lander. However, by far the best data for finding the lander will be the CONSERT instrument, which has a part on the lander and a part on the orbiter. CONSERT works by transmitting radio signals from the orbiter to the lander in order to study the comet interior, but can also be used to help identify the location.
I'm quite new to this site, so I can't comment on the answer posted by Hobbes, but there is no Star Tracker onboard Philae. The wikipedia section he was referring to seems to have been a copy/paste error by somebody and was refering to Rosetta orbiter instruments, not the Philae lander. Star trackers are used by spacecraft to determine their attitude, for purposes of navigation. Since Philae has no navigation ability, it has no need for such equipment. The surfaces of Philae are optimised for its mission, i.e. they are covered in solar panels and two passive thermal absorber foils, with the exception of the backpanel ("balcony") which is dedicated to instrument units.
Also note that a star tracker wouldn't work on the surface of the comet anyway. Rosetta has had problems with its star trackers getting confused by dust, and the environment at the surface would be so much worse they would be unusable.
Philae does have a panoramic camera system (CIVA) but the images this has provided have been far from conclusive when it comes to identifying the location of the lander.
As of June 11th, it is still unknown according to this ESA blog post:
Rosetta and Philae teams continue to search for the current location of the lander, piecing together clues from its unexpected flight over the surface of Comet 67P/Churyumov-Gerasimenko after its initial landing on 12 November.
However, I understand that it is looking likelier that Philae will be found now that it is transmitting back data again. At least the fact that its solar panels are generating power means that Philae is in the sun (periodically) and thus casts a shadow of itself, which should make it stand out more clearly in the surface pictures taken by Rosetta.
Doppler shifting between Rosetta and Philae's transmitters could in theory be used for mutual tracking... however Rosetta's orbital velocity is very low, so I think the answer is a firm "No", unless perhaps Rosetta can be risked making a few more low passes.
The only real chance I think is to get some pictures back from Philae, of its surroundings, and try to eliminate all possible locations by comparison with Rosetta's pictures. A few possible locations are described in this post: