I'm looking for some new places to spend time hiking/biking near the city. Right now the only good area I know of is near Bamboo Temple. If you go there, you can find some nice secluded trails with decent scenery. Unlike the inner-city parks, you can do a 360 degree turn without seeing or hearing anyone.

Are there any other places near Kunming like that which can be reached and returned from in a day?

I believe this question has passed the forums many times already. Try the search option.

There are a couple of nice rides north (changchongshan to dashao then east and down again), northwest (fumin) and south (wetlands). If you're fast, also Aziying and places further north can be done in a day