Círdan probably the longest living elf in Middle-earth has been on Middle-earth since the days of the Two Trees and is the best ship builder of the Elves. 

It is interesting that he never left for Valinor first when Morgoth was defeated in Beleriand, then when Sauron was defeated both in the Second and Third Ages. 

Did he not want to leave Middle-earth because he's been there so long?

Did Círdan ever depart from Middle-earth or does he not wish to cross into the West and forever stay in Lindon?