I am in Hamburg about 8 or 9 times a year.
If you like sweet shots, visit Albers Bar, it has shots that taste like strawberries and cream or apple strudel.
If you like beer, visit Altes Mädchen - they have something like 60 beers, something like 20 on tap and they brew their own too. Do some decentish food also! Every time I am in Hamburg I visit at least once.
If you like steak - Estancia Steaks is pretty good
If you're trying impress, probably somewhere like The table Kevin fehling, Delta bistro or Meatery.
depends what you're doing really dude, I am usually there eating/drinking with clients/friends/colleagues