I was through Bremen yesterday. The Atlantic hotel is right at the terminal, but priced accordingly. You can easily take the #6 tram downtown where there is ample choice in hotels.
Also consider flying up to Bremerhaven. Good hotels here too, and lots of things to see and do. This airport is scheduled to close, so see it while you can! A ride is necessary from Bremerhaven airport to the city though, as it's about a 3km trip.