Perhaps I am an anomaly, but I'd rather not be doing dishes and laundry when I travel for leisure and relaxation. Traveling for work is another matter. I look to be pampered when I am on vacation and happily pay others to do things I have to do for myself when I am home.
I really think if you decided to go to one city for 3 weeks or a month, you'd love a place that's a little more a home. I admit it might not work for me, I've never, as an adult, stayed in one city on vacation for more than a few days.