travel to qingdao,shenyang, jinan,beijing trip

Good afternoon to all ,

Since this is my first trip to visit the north of China, I was hoping somebody would give me suggestions on how to fly to these places economically and efficiently.

I am planning a trip to qingdao, jinan ,shenyang , beijing this middle of august. Need help on how best to fly to these places and which city should i go to first and so on and so forth.

I plan to fly to all of these places and start my trip from shanghai and to fly back to shanghai from the above places.

I will be having an overnight stay at each city and will continue traveling the next day onwards.

can anybody be so kind as to direct or guide me which places I should visit first and what airlines to take going to these places.

I would really appreciate any advice or suggestion .

thanks in advance,

Max