I had a friend who had both a family room and a living room. Most newer houses in Winnipeg have this sort of distinction. Living room has the nice furniture, used when people come over. Family room has the TV, video games, and all the mess. Our house was old enough not to need such a distinction. A rec room to me is necessarily in the basement. (Not sure why.)

The area adjacent to the front door is "by the front door" for me, usually. A bit unsophisticated, I guess.

As I was growing up, and we switched around the contents of two ground-floor bedrooms, there were rooms which were sometimes the "piano room" (so as not to annoy the rest of the people in the house when playing) and the "computer room" (obvious). The piano and computer were, for a time, together in a room. Much later both were removed but the name stayed with the room. In my new place we have a "study" with a computer, no piano, two bass guitars, a guitar, a violin, and a trombone, but for some reason I still call it the "piano room". Luckily my husband was familiar with my old house - otherwise it would be very confusing!