Two layovers in China, Shanghai and Kunming

I'm travelling to Nepal from Hawaii as a US citizen. I have only a five hour layover in Shanghai which I probably won't leave the airport, then arrive in Kunming late that night. Is it possible to leave the airport in Kunming to get a nights rest at a hotel, or am I better off staying in the airport if I don't have a visa. Also, the Nepal visa is issued in Nepal and so I won't have it until I arrive in Kathmandu, is this a problem for the 72 hour free transit?