(question from a CSer) For me (probably us) is mainly to get lost in the streets, try to see a bit the main monuments. Sometimes to see a temporary exhibition going on, someother times trying to find things (bar, places) we like and which are not in the guide book. So, basically, walk.
When we are monte in the countryside we like to explore a National Park by bike or hiking or kayak.
With Couchsurfing also talking with the host is an important part, to talk about everything and nothing, to experience their house, meet their friends, cook for them. This includes to go to supermarket, buy a SIM card, understand how the country where we are works.