Nordaggio's Coffee is a great little cafe located in south Tulsa, near Oral Roberts University. I bring my dog with me there frequently, to lie at my feet while I work. The staff is really great about it. The cafe is frequented by a lot of college students, who love seeing (and petting!) a dog in there. I've been told the owner is a dog-lover. You can sit outside at tables, or inside the cafe itself.