Ummm...I don't know if I have one. I don't think I have a place that is the one place that I just like to go hang out. If I had to pick a place that I particularly liked, it would be the Twilight Grove in Duskwood. I leveled through that zone a couple times before I ever actually explored it and was amazed at what I found when I went there. I definitely have some favorite zones.
For classic WoW, I definitely loved Ashenvale the most, even if I was initially afraid of it. The music and the locations are just my favorite. There are some fallen trees that you could get on that went over the road that I loved to climb on. I still haven't actually leveled there since Cataclysm came out (I'm way behind on things) and am eager to check it out, even if it will make me sad. Duskwood. For Outland, I love Nagrand with its scenic beauty the most. In Northrend, the Grizzly Hills were my favorite. I love the Furbolg. The music for the Grizzly Hills was what really got me excited for the zone before Wrath even came out. In the Cataclysm content, I'd have to say that I like Vash'jir the most. The zone has great history, views, and it's just so big and mysterious.
Out of game
My parent's house has this one room that I absolutely love. If you never looked in it you'd probably just think it was a closet. It's a narrow room, probably 5 ft wide by 7 ft long. It has a narrow entrance at one end and at the other end the room narrows into a little alcove that has window. On one wall there is an old desk with a couple shelves above it and a light attached to the bottom of the bottom shelf to light the desk. This cozy little room has always appealed to me, and I spent a good amount of time studying in there.
In the future, I'd like to live somewhere that had one room that was no more that 10 ft by 10 ft, with windows covering half the room and bookshelves covering the other half. There'd be a window seat in front of the windows with pillows on it, and possibly a small, simple desk somewhere. It would be my favorite room.
When I have a house someday, I want it to have a bunch of small, intimate, specifically designed rooms instead of a handful of large, general purpose rooms. It's probably because I'm such an introvert.