I really don't think we need any new culture buildings at this point. I'm in fact concerned with how many we do have.
BTS has exactly 6 non-religious, non-Wonder buildings that provide culture: Monument, Library, Theatre, Castle, University, and Broadcast Tower, and two of those are obsolete before the end of the Renaissance.
In AND, the equivalent culture levels are 4.8 times that of BTS. A Normal-speed game is 2.4 times longer (1200 turns vs. 500) but that still leaves a 2x modifier. So it's OK if we have more culture from buildings, but there is a limit. I count over 50 buildings that generate culture, and even though there are replacements and some go obsolete, there are still 30 building lines that generate culture.
For comparison, in BTS, a fully tricked out city at the end of the Modern Era can generate +12 culture from buildings alone (+2 from Library, +3 from Theatre, +3 from University, +50% from Broadcast Tower). In AND, we could get up to +99 culture (+6 from Art Gallery [includes +2 from Modern Art], +2 from Casino, +3 from City Park, +2 from Library, +4 from Metropolitan Administration, +2 from Monument, +1 from Museum, +5 from Movie Theatre, +3 from Naval Academy, +3 from Opera House, +2 from Photographer's Studio, +1 from School, +4 from Stadium, +3 from University, +4 from Vacation Resort, +2 from Zoo, +10% from Advertising Agency, +10% from Museum, +10% from Press Agency, +30% from Communication Tower, +50% from Convention Center). Again, this is not counting religions, Wonders, or specialists.
There are two things I would like to do: reduce Scriptorium to +1 culture (it's currently +2) and do something to rein in Naval Academy. Yes, Military Academy provides +3 culture, but it's also extremely limited in that you have to sacrifice a Great General to get one. Naval Academy has no such limit, and I think it provides too large a bonus for an unlimited building. It not only provides +3 XP, but also Navigation I, and the free promotion doesn't count towards increasing the XP requirement for the next promotion, so it's a minimum of +5 XP. I'd like it if Naval Academies were only buildable once per Military Academy, but that can't be done in the XML; since building scaling applies to every non-Wonder building, going up to Huge size means you need 2 Military Academies per 1 Naval Academy and that is too high a barrier.
I agree that Music is on the weak side as far as technologies go. I'm considering moving Tavern up from Monarchy to Music. Monarchy has 6 tricks and could spare one.