We ate dinner at almost all of Disney's Signature Restaurants in February and I didn't find any of them to be very noisy (and this is something that bothers me about most L.A. restaurants).
The secret is to make early reservations. Almost all of ours were 5:30ish, or right when the restaurant opened, before the crowds showed up. We had a lovely quiet meal at California Grill, even! This also kept us from feeling rushed at most places (Le Cellier excepted) and from having to wait a long time to be seated.