How many days to cover most places of interest in Qingdao? Any itinerary or land tours to recommend?

Hi, three days are enough to cover almost attractions there. Here is a suggestion for the itinerary for your reference:
Day 1: Mt. Laoshan - Zhanqiao
Day 2: Naval Museum- Small Qingdao - First Bathing Beach
Day 3: Badaguan - Luxun Park - Christian Church. If time permits, go to the Wusi Square.

I joined a tour arranged by Travel China Guide in 2012, with six other travels in our group and it was amazing. If needed, here is their contact: tourstravelchinaguide.com

may help!