Well as has been mentioned - Elrond would have been far too conspicuous and -after all Gandalf was already going - but also Elrond and Galadriel keep their lands safe by the power in themselves and of the rings they wield. If Elrond leaves, Rivendell is vulnerable and the quest is no more likely to succeed.
Avie - I really thing you are being grossly unfair to Elrond - if he was only concerned about himself he would have "nanced" off to the Havens long ago, and rejoined his beloved Celebrian. HE stays to maintain Imladris as a last stronghold and refuge - open to all the free people of ME not just the Noldor. Given that the whole mess was caused by not following his advice, it is quite decent of Elrond to get invcolved at all...
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“But Finrod walks with Finarfin his father beneath the trees in Eldamar.”
Christopher Tolkien, Requiescat in pace
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