Yes :) Unless for some reason you're talking about a room that is alive, in which case 'room' is a noun and 'living' is an adjective.
But if you're talking about a 'living room' like the actual room that is called that, then yes it is a noun.
Living room is an adjective followed by a noun. Here's the test. Room is a noun because it fits the definition of a noun "Person, place or thing." room is a place (or thing, a room could be a thing). Then, you follow the definition of adjective, which is a word that describes a noun, by asking the question "What KIND of room?" If you can answer that question without it seeming weird to you, then it's an adjective. What kind of room? "Living" room. If it was a different room, like where you eat, then the adjective would be "dining" room, likewise with recreation room. Now, if you have a situation where the word is a compound, like bedroom, the whole thing is a noun because it is used in a single word.