Not sure if this is applicable since it's technically about places out of Ningbo, but it might be considered relevant. My personal favorite place is Wulongtan, followed by Xikou probably. I guess i got a thing for waterfalls. They're more expensive and longer drives than a trip out to say, Dongqiang Lake, but are also more removed from the city and cleaner. When all I see is the murky downtown rivers every day, it's a relief to meet blue pools and clear streams.
day trips? Wu Long Tan for sure. Swimming in the pools under waterfalls and having apicnic on the river bank, very nice. A weekend camping is harder to pick, but an island of Xiang Shan called Yu Shan Lie Dao is pretty wicked, no cars when I went there a year ago!