We used to guide in other locations outside of Berlin, but now we focus on the city itself. Nonetheless, here are some ideas for things to do outside of Berlin, especially if you're the kind of travelers who come to Berlin for a longer stay:
Many visitors ask us to guide them in Potsdam. However, Potsdam lacks the complexity, importance and historical depth that are so characteristic of Berlin. We therefore believe that you could easily cover it without personal guidance (and we don't like to be paid for no good reason). It is actually better to visit Potsdam independently, as this visit is mostly about walking in the royal gardens and strolling through the streets and alleys of the picturesque old town.
We recommend that you take your time and do all that at ease. You could also take one of the hop-on hop-off tourist busses to get to the various palaces, which you could also visit on your own (external guides are not allowed to guide there anyway). Most tourists only visit Potsdam's most famous palace Sanssouci (it's not that easy to do more than one palace on a single day), but you might be more interested in visiting the mansion of Cecilienhof; though not very close to the old city, we think it is historically more important than the other palaces because of the Potsdam Conference that took place there after the 2nd World War (with Truman, Stalin and Churchill, who later on was replaced by Attlee during the conference): www.spsg.de/en/palaces-gardens/object/cecilienhof-palace/
We also recommend visiting the Barberini art museum, located in between the train station and the old city. Check out their website for information about current and upcoming exhibitions.
When strolling in the old city, don’t miss the Dutch quarter and the Apfelstrudel served at La Maison du Chocolat – Potsdam’s house of Chocolate: www.schokoladenhaus-potsdam.de
In previous years, we also used to guide in the former Nazi concentration camp of Sachsenhausen, located north of Berlin. But we don’t anymore, specifically because of the long time it takes to get there (more than an hour, often about two hours for each direction).
If you do want to visit the former camp, you should take into consideration that not much is left there. Nowadays, the space itself is almost completely empty, except for a few monuments and several exhibitions focusing primarily on the horrible conditions in the camp and the inhuman methods practiced there. There is also a separate exhibition focusing on Jewish inmates.
Nevertheless, it is of course a place of great historical importance and if you have the time for such a day trip, we would recommend doing so with the non-profit tours organized by the Friends of the Sachsenhausen Memorial:
Further away, about 3 hours for each direction, is Dresden, famous for its reconstructed old city and its art museums. As it's half way between Berlin and Prague, we usually recommend visiting Dresden on the way from Berlin to Prague or vice versa, but you can cover the old city and one or two museums with a day trip from Berlin, especially on long summer days.
At about the same distance but in the opposite direction is Hamburg, which is an important city in and of itself. It has much more to offer than Dresden, so we would recommend spending a night or two in Hamburg, but a day trip is doable.
On cold days you could take a train to the Tropical Islands resort in the East-German countryside, quite close to Berlin (great with kids):