Athlete Ally, where Quinn is a board member, will honor Jason Collins and Martina Navratilova.
The proposals, first suggested last year, would share more power with the City Council membership.
Christine Quinn was a top choice for CEO of the struggling AIDS organization, sources said.
The legislation, passed on Tuesday, will require the city to install speed humps near schools.
Mayor Bloomberg yanked the proposal after the City Council rejected it.
Bill de Blasio will be the first Democratic mayor since David Dinkins was elected in 1989.
The measure also raises the age to purchase e-cigarettes.
A plan to give city council members more power has racked up 30 signatures so far, organizers said.
The legislation prohibits employers from discriminating against pregnant women.
A group of members wants to shift some of the next City Council speaker's power back to the council.
City Council Speaker Christine Quinn, once a front-runner, urged New Yorkers to vote for Bill de Blasio.
Two days after losing her bid for mayor, Quinn promised "a ton" of Council activity in her last months.
The cermony drew loved ones of the 274 Staten Islanders killed.
Results showed Bill de Blasio within a razor's edge of winning the 40 percent needed to avoid a runoff.
Johnson defeated civil rights lawyer Yetta Kurland to win the Democratic nomination for the seat.
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