independent travel without hotel reservations and which "entry" type is best

I am planning to travel independently throughout China for several months on a tourist visa. I will have a roundtrip ticket but am not sure how I would prove that I have hotel reservations since my plan is to find hotels as I travel. Also, I would like to get a visa that allows me to stay for as many months as possible, even if I have to leave the country (ie go to HongKong briefly) and then re-enter. Should I ask for a multiple entry visa and if so do I need a letter explaining why I want that type. How long would a double entry visa allow me to stay? I have visited China previously on a double entry student visa but this is my first time on tourist visa.