The monthly Deutschlandticket (deutschlandticket.de) seems like a pretty good deal if you plan to travel more in some region of Germany (seems it includes all public transport in cities and regional trains). Of course, nobody bothered to translate their site in English...
@bbatsov it is a good deal! It's not designed for tourists though as it's on a calendar month basis. As usual in Germany, everything has to be more complicated than necessary. You'll want to buy it from a less strict provider than DB, try the "mo.pla" app. They let you cancel it on short notice.
@Odaeus Thanks for the tip! I was wondering about that as I noticed their apps are only on the German Play/App stores. Is there some other alternative for week of travel with regional trains? I’m staying in Hamburg for 10 days and I want to visit some nearby towns.
@bbatsov hmm, HVV.de is the operator for Hamburg local services. Even their app is not available? Because they offer a weekly pass (https://www.hvv.de/en/tickets/weekly-monthly-tickets/24-7-season-tickets-site), but you'll have to check if your destinations are covered in their zone. Otherwise I'm not aware of any other passes. Often there are discounted tickets, e.g. for a day return or group travel.
24-7 season tickets

HVV - 24/7 season tickets

Hamburger Verkehrsverbund
@Odaeus I’ve managed to get a monthly ticket via https://www.hvv-deutschlandticket.de/en/
hvv Deutschlandticket

Travel all over Germany for € 49 a month with the hvv Deutschlandticket.

@bbatsov do you plan to come to Lübeck?
@chipollino We were there yesterday - amazing city!
@bbatsov oh no! Have you waited to not disclose you location? :)
I could give you local tips.
@chipollino Local tips are always welcome! I’m hoping to be back to Hamburg and Lubeck for the Christmas markets. (Might even spent a couple of nights in LubeckI really liked the region and I’m guessing the Christmas markets here are pretty good!