Miniatur Wunderland is a great visit even before this.
Don't let the 'model railway' bit put you off, it is one of hamburgs top attractions. Their models usually have masses of humour all over them, from alien landings, to bank roberies, to porn scenes being filmed.
When I went the visitors were of all ages and sexs, from groups of young femal backbackers to guys on stag weekends, kids groups, elderly. All getting on perfectly and enjoying the experience together. Seriously, don't let any steroptype put you off going to see this.
[Incidentally, I think HAM airport itself still has it's own model airport at the airport (no where near as good as minature wonderland, but worth a mention).
http://www.airport.de/en/airport_model_exhibition.html - oh and look at the picture at the top of the page closely. Stress: This is NOT minature wonderland.]