The various Recreation Rooms seem to be the ship's social hubs with singing, games and other entertainments.
The ship also boasts an extensive dojo and sports facility
In the Animated Series, the Enterprise had a moderately advanced hologram suite, one capable of producing rural, coastal and arboreal scenes with realistic sounds and wind.

The factbook Mr Scott's Guide to the Enterprise features a wealth of information about the amenities available on the ship's 'Rec Deck'
Enterprise's rec deck is the largest and best equipped of any in Star
Fleet. Off-duty crew members will find a variety of games and pastimes
from which to choose within its walls.
At the front of the room is an immense, wall- mounted viewing screen,
the largest aboard ship. This three-dimensional imaging device can be
programmed to display any one of thousands of twentieth-,
twenty-first, or twenty-second century movies, and also holds in its
memory a lesser number of twenty-third century releases. Live sporting
events, carried by subspace video comlink, can be displayed as well.
On rare occasion, the unit is used to display Star Fleet Personnel
Address broadcasts for crew assemblies.
Beneath the viewing screen is an information display alcove. Five
small screens exhibit, upon request, a choice of pictorial histories,
including those of Star Fleet, the Federation, the countries on Earth,
Vulcan, Alpha Centauri, and other Federation worlds, and all vessels
which have borne the name "Enterprise." Reading lounges and snack bars
line the port and starboard bulkheads.
Restrooms, designated "male" [portside] and "female" [starboard] for
the convenience of non-crew visitors, are located near the rec deck's
rear wall on the lower level.
Two turbolifts on the forward end of the room provide access to F Deck
and the rec deck's balcony around. This upper area houses smaller
rooms where three-dimensional chess and checkers may be played, as
well as cards, backgammon, and other non-electronic games.
A raised platform in the center of the lower level floor features a
diversity of electronic entertainments. Games such as Concentrex,
Challenge, Eye-Q, and Phaser Duel are programmed into consoles which
stand within sunken seating areas. A shufflelight board in the middle
of the floor may be used for tournament play.
Eight immense viewports in the rec deck's outer wall give crew members
an unspoiled view of the ship's secondary hull and warp nacelles, and
are useful for planet observation while Enterprise is in standard
orbit.
