That's a tricky one - not aware of a website, certainly for stage musicals, but you may wel find a non-official fan-site. For filmed musicals you couldn't really better imdb.com - then just use the cast lists for each film.
There are excellent reference books published on musicals - I have a couple of very hefty tomes (I think one is the Virgin guide) and they are pretty exhaustive.
Have you tried typing in the web... One Look ...and going on One Look Dictionary..........I then type in the name of the musical / play and go into Wikipedia, that's usually quite helpful!
PS
If you're into the crossies..........try the reverse dictionary function on this site.