Some of that can be found in
Black Heaven (keyboards and drums; not sure if you get to see hands close up for the keyboards, it's been a while since I watched it.)
For something currently airing, there is
K-On! for keyboard (definitely see hand closeups) and drums.
Beck also showed drum playing.
Chrono Crusade should have at least one choir scene.
Also
Trinity Blood.
There is a good chance that any anime with a character dressed as a nun or set in a Christian/Catholic school will feature a church choir. And possibly a church organ. Possible suspects:
School Rumble (very vague, you might have to search through many episodes, memory is bad),
My-HiME (my memory is also bad),
Maria Watches Over Us (never seen it, total shot in the dark).
And it's been a really long time, but I could swear
Sailor Moon had a church organ in there at one point. I know
Revolutionary Girl Utena had piano playing; can't remember if there were organs too.
Checking
tvtropes.org, Kagato in
Tenchi Muyo! is introduced playing a futuristic organ.