I would take a serious look at Yale div school—the conversation is definitely happening there. Faculty-wise Kathryn Tanner is there and does some of that and Linn Tonstad is going there in the fall from SMU. Tonstad is young, brilliant, and queer theology is her wheelhouse—definitely someone to check out if you want to do queer theology (emphasis on the theology) rather than just bringing queer critical theory to the study of religion.
Union Theological Seminary is also a great place, but is more focused on MDiv's.
HDS is of course a lovely place, but be warned: with Mark Jordan leaving and Marie Griffith already gone, there might not actually be anyone to teach queer-ish things.
It can be done at Claremont Graduate University too, but good luck getting funding.
Don't know about Vanderbilt faculty, but it would be worth checking.
Here at Chicago div school we have a nascent queer theology reading group, but this is probably not the place if you want queer theology to be your focus (with Tanner gone and our refusal to hire Mark Jordan).
All in all, from what I know (very little!) Union and YDS are the two places where queer issues are at the forefront, but I think that at basically any good div school (other than Chicago) it would be possible. I'm sure that others on this board have some more info. Happy hunting!