From what I understand, which may be very little, you cannot publicly announce that you are going somewhere and want to split costs. But you can privately ask other pilots, and chances are word will get around.
If they're both legal to be PIC and looking to split both the flying and the costs (i.e., each one pays for and logs only the flying s/he does), there's nothing illegal even without "common purpose". However, I don't know of any such web sites.