I've said this earlier, but I've given it some more thought.
I'd like to see an annex to City Hall (I'm envisioning glass cube forms, echoing City Hall but appearing much lighter--this would also pick up on the Holocaust Memorial close by) on the Congress Street side stretching back onto City Hall Plaza for public service functions: permitting, paying parking tickets, etc. which would include a museum space/visitor center. The glass cube idea could also be extended to enclosing the entrance to City Hall.
I'd take the space in the lower levels of City Hall which currently serve the public and give them over to a library for the BRA/Environment Department--any agency which produces documents that the public might like to see on a regular basis--old planning reports for example, or Boston Landmarks Commission files--and possibly include some space for the Boston Archives to have some of its most in demand materials, or a BPL sponsored reading room of Boston history. Given the storage problems of materials faced by the BRA and Environment, I think this would also go a long way to helping improve those office spaces as well.
I'd leave City Council, the BRA, the Mayor's offices, etc. in the old building--they have some great views of Boston and the waterfront. I'd bring in a lighting consultant to redo the lighting throughout using energy saving LED lighting. A restaurant on the roof? A roof garden? Sure, why not?
Finally, I'd give City Hall Plaza over to some housing/retail, the year round farmer's market perhaps, using the lines of old Scollay Square as an inspiration--to help finance the annex. The National Park Service would probably chip in some financing for the visitor center in the annex and it would help solve the Boston Museum Project's biggest problem, which is a phenomenally expensive site on which they hope to build a museum. I'd leave space from the Gov't Center Station looking towards City Hall to preserve something of the open space which gives City Hall its iconic stature.
I believe this plan solves a number of problems currently on the table in Boston. And, of course, it will never happen.