Berlin is a huge city but you can easily get around by public transportation, even with a stroller.
It is easy to get around Berlin as most of the U Bahn (subway) and S-Bahn (city rail) stations which connect the main tourist sites are stroller accessible and many have elevators leading to the platforms. Where there are no elevators you may need to carry your stroller up and down some steps. All tickets can be used on any part of the system. The public transport system (U, S-Bahn, bus, tram) uses a common ticket. A two hour ticket allows you to hop from bus to U-Bahn to S-Bahn to tram for the modest price of 2.40 Euros. Simply purchase your ticket from the machines on every platform and get it validated in the box next to the ticket machine, before you board your transport. The U-Bahn and S-Bahn system operates from 4 o clock to past midnight but On the weekends, most U-Bahn lines run at night as well. See www.s-bahn-berlin.de for routes and for information on stroller accessible stations.
There is also a tram service in Berlin city centre and the city is well connected by a local bus service. The hop on hop off tourist buses are also a great option and if you buy a two day ticket you will be able to see all the major attractions (please note that most of these buses stop running at 6pm).
The city itself is very walkable and stroller friendly as it is very flat, with wide footpaths. You can also rent bicycles in many places with toddler seats mounted on the back. This is a great option for exploring the city as there are plenty of bike paths. It is particularly good if you plan to go to the Tiergarten area (the large green leafy park in the centre of Berlin in front of the Brandenburg Gate). The bike rental shop may be able to store your stroller while you explore!