"Towns in Brandenburg just outside of Berlin suggested to me that I recall are Teltow, Stahnsdorf and Falkensee. There were mixed opinions about Kleinmachnow which I never quite got to the bottom of."
Eh, we live 100 metres from Kleinmachnow and I've never thought there's much of a problem. KM is Berlin in all but name. I know lots of non-Germans there - nobody has ever had any sort of hassle. The Real supermarket is pretty dodgy though.
As far as Stahnsdorf is concerned, we nearly bought a house there in a new estate 10 years ago (and then went for a smaller place in Berlin, just, instead). We asked the Makler if there were any other non-German families on the (large) estate, and he struggled a bit but then came up with one family with a Turkish father and German mother. That says it all. Apart from that I know two Canadians who live in Stahnsdorf (separately) but both are married to Germans.
DH teaches in higher education in Brandenburg and finds it pretty dire in terms of prehistoric attitudes. What part of 'south of Berlin' are you from? So much of it now is in the commuter belt, and generally speaking if you have an English-speaking child in KM or Potsdam you will be allowed to use Berlin schools (my DC go to school with several Brandenburg kids - the Berlin school system is bad, but still preferable to Brandenburg). There's a private English school in KM and several state schools in Zehlendorf (PM me if you want to know more about them).
Generally speaking, Germany is a great place to be bringing up kids, and around Berlin is a good place because there are far more options for childcare than in eg Bavaria. I was in a village outside Munich last weekend and it was lovely but a bit Stepford wives-like.
I know of one Kita which might be interested in taking you in Zehlendorf, if you could go along with Montessori ideas and be prepared to do a berufsbegleitetes Studium.
Caterpillar - "I was strongly advised to stay clear of the former East Berlin (except places like Prenzlauer Berg where you do have some multiculturalism on an affluent level) and all of Brandenburg except for places that have seen an influx of people from other parts of Germany since the Wende."
Sad, isn't it. We spend a lot of time exploring Brandenburg, but would certainly be less keen if any of us were mixed race.