Hainan Airlines sponsored my flight from Berlin to Beijing. I had a very good experience onboard with great comfort and service. I also liked the fact that I could charge my laptop onboard, which is something you can only do on very few airlines. Hainan Airlines flies to the following international destinations from Beijing: Almaty, Bangkok-Suvarnabhumi, Berlin-Tegel, Boston, Brussels, Chicago-O'Hare, Denpasar, Irkutsk, Malé, Moscow-Sheremetyevo, Phuket, Prague (begins September 23rd, 2015), San Jose (CA), Seattle, St. Petersburg, Taipei-Taoyuan, Toronto-Pearson.
Not many people know about Hainan Airlines, but it is definitely one of the best 200+ airlines I have flown and much better than any Chinese airline. I can highly recommend them and on some international routes they might even have the lowest fares.