Do whales ever just hang out on the surface breathing?
Whales often hang out on the surface for a while, for a number of reasons. Sometimes it is for curiosity, sometimes to socialize with other whales, and sometimes simply to rest.  The particular sort behavior that you are describing sounds like logging, where the whale basically rests, often for an extended period of time, with its back slightly out of the water, looking sort of like a floating log.