Last Sunday we took advantage of the surprisingly good weather and walked through Baumanskaya region with Olga. In fact, before 1920th the place has been called "German settlement" and for centuries has been the foreigners quarter in Moscow.
Luckily, it's not as much destroyed by Moscow renovations as central districts, so you can still find there multiple wooden houses (including the one of Vasily Pushkin, uncle of Alexander Pushkin), palaces (Lefort Palace is the most famous, but not the only one), very splendid rental homes from beginning of 20th century, constructivism buildings of 1920-30th, plus multiple gardens. We wandered there for 5 hours and still could explore only the tiny bit of this amazing area. Also, enjoyed eating "pirozhkis" in the quiet garden of Great Martyr Nikita temple, and my smaller niece loved the "Pushkin fairy tale" playground at Pleteshkovsky Lane.
We highly recommend you to explore this area either with our guides or on your own.