any of the pubs/clubs down the grassmarket or cowgate area are hoaching with young people up for a good time. Also there are now loads of nice bars along George Street and in the surrounding areas at the start of the new town.
If pulling someone in a club is not your thing then there are bound to be dating agencies there too, but the best bet is just to get out there and spread yourself about a bit.
If you're just looking to meet people to hang around with as mates then why not join a gym/sports centre/arts class etc. etc.