media snug
n. A small, comfortable room or space to read, watch, play, or listen to media.
Examples
2016
A horrible estate agent's neologism: the apartment contains 'a media snug'.
—Jamie Muir, “A horrible…,” Twitter, January 16, 2016
2015
A book-lover's lifetime collection. Many guests say the library or media snug is their favorite room.
2013
Our @lunadesignuk showroom media snug with products from @ArtcousticUK @Control4 @BeB_Italia pop in for a listen.
—Smart Home Sounds, “Our @lunadesignuk…,” Twitter, June 21, 2013
2012 (earliest)
Notable Inclusions : a stunning dining hall central to all ground floor rooms; …an exciting media snug.
—“5 bedroom house for sale,” Rightmove, August 22, 2012
Notes
A snug is a small room or space that is cozy, comfortable, and warm. It most often refers to a small bar-parlour in a larger inn or pub, but it gets plenty of use as a reference to a cozy den or comfortable lounging area in a house, apartment, or lodge. It's short for snuggery, a term that dates to at least 1727 (the OED's earliest is from 1812, so this is a significant antedating).