This is a map that appeared last week in a story published by Maariv on Jews in "east Jerusalem". I have added the correct Hebrew names of the communities and even added Neveh Yaakov, although there are a few others, too, that were left off the map, like: Ramot Eshkol; Givat HaMivtar; French's Hill; Ramat Shlomo; East Talpiot; etc. - why they are absent, I do not know (one of Ir Amim's list; and a map of their's;)
One source of the demographics is here:
At the end of 2008, the population of East Jerusalem was 456,300, comprising 60% of Jerusalem's residents. Of these, 195,500 (43%) are Jews, (comprising 40% of the Jewish population of Jerusalem as a whole), 260,800 (57%) are Muslim (comprising 98% of the Muslim population of Jerusalem) [*].
That is a bit low.
The map above has these figures for the Jewish population:
Gilo - 32,000
Har Homa - 20,000
Nof Tzion - 75 families
'Muslim' Quarter - 1000
Ir David - 60 families
Maaleh Zeitim - 110 families
Shimon HaTzadik - 15 families
Ramot Allon - 46,000
Pisgat Ze'ev - 42,000
which totals 141,000 + 260 families (c. 1000) which leaves missing some 50,000.
Going here (in Hebrew), I found the Statistical Yearbook which adds, as of the end of 2009, 2400 Jews in the Jewish Quarter; 18,600 in Neveh Yaakov; 14,200 in Ramat Shlomo; 10,300 for Ramat Eshkol/Givat HaMivtar; 13,700 in East Talpiot and there are lower discrepanices for other neighborhoods mentioned. But more than the "missing" 50,000 is there. And that was some two years ago.
All of which, at the end of this, makes for an exercise in poor research.
P.S. Do not forget, before 1855, there were no "neighbohoods" except within the Old City walls and the Jewish population was the majority already by 1853.