It would help if you specified which birds that are - many of the birds that are considered "regional specialties" around Berlin (Bustard, Hoopoe, Crested Lark, ...) can be seen equally well, or better, in Spain, because of similar terrain. FWIW, I've seen Great Bustard in Castilla and León (from the train, no less), but not yet in Germany.
For Great Bustards, apparently the best spot is the
Havelländisches Luch (especially Buckow near Nennhausen - there are several places called Buckow, so be careful you get the right one). This place, according to the description, is also good for a number of other species, including Grey Partridge, Ortolan, Barred Warbler, and numerous wetland species - if you want to know more details about the species and access, run the description through Google Translate, or ask here). Definitely worth checking out if you have the time. It's probably best to get a car, though, if you plan on going there.
As for other places, I've heard that the National Park "Unteres Odertal" (Lower Odra Valley) is also very good for species like Lesser Spotted Eagle, Black Stork, Black Tern, Corncrake, River Warbler, possibly still Aquatic Warbler, Red-breasted Flycatcher, etc. (see previous threads on Berlin).
Personally, I've been to the Döberitzer Heide this summer. This one is accessible via public transport (bus). Species I've seen there in one day include Barred Warbler, Hoopoe (probably less exciting for you, but in Germany, it's a huge rarity), a ridiculously large number of Red-backed Shrikes, Honey Buzzard, Osprey, Wryneck, Tree Pipit, Wheatear, Sand Lizard, and so on.
Berlin itself has urban Goshawks and a number of other interesting species.
N.b. - I'm not sure which of those species have already left for their wintering grounds. Rosefinches are definitely already on migration, for example.
