Whether or not a Dane would do well in an apartment I think really depends on the people and particular dog. I would hate it, but I'm used to just letting my dogs out to potty! You have to be realistic about how much you're going to want to take the dog out potty, and out to parks, etc. Do you have good dog parks near you? Also doing doggy day care 1-2 times a week, or hiring a dog walker, can be a huge help!
Its so funny to me how much is ingrained in breeds as far as personality. Every Dane/Lab mix I have met is such a clear combination of the two...goofy, leaners, but with the lab energy and ability to fetch. Danes...not such good fetchers!!
Also you have to think about what you'd do if you have to move. Not many apartments or rentals accept big dogs!