My favorite, somewhat quiet spots are:
1) Game/card room behind Safari Club
2) Cinema for an afternoon movie
3) Seaview as noted previously for snacks in the afternoon and late night.
4) Concierge Club, if you have status or have the right room
5) Back of windjammer on deck
6) Balcony cabin patio - given no one is smoking next door
These aren't really secret, but are still nice.