The old German quarter, the main beaches, and the Tsingtao Brewery are all within walking distance of each other and of the old Qingdao Station. This part of the city is very walkable. For the Museumsmeile-equivalent sights further north — the modern downtown around Taidong and Shibei — the metro is the sensible choice.
Qingdao Metro has several lines and is clean, cheap, and easy to navigate with the help of a mapping app. Buses cover the city but the network is complex. Taxis are plentiful and reasonably priced; insist on the meter.
The hill parks of the old German quarter are best explored on foot; some slopes are steep enough that comfortable shoes matter.