I went with a fairly modern chaise lounge, somewhat similar in shape to this but a bit sleeker:
While it takes up a fair amount of space, it's the most popular seat in the house...for both people and pets. It's been nicknamed "the comfy chair". I had it in my living room for a time and never got to use it; it was always occupied. I finally moved it into my office, which is off limits to everyone else, and that way it's reserved for just me. Except for my evil tuxedo cat, who's pretty sure it's hers.