Is this your first time in China? Here's what I would do.

Couple of nights at the GH HK. Rates here tend to be highest amongst all Hyatts in China, so this would be a good place to use your Chase nights. The vibe here tends to be a little more business as compared to the HR TST, which is more touristy. That said, I personally prefer the GH to the HR TST as it's just a better looking hotel.

Next I would spend at least three nights in Beijing. One day for the Great Wall, one day at the Forbidden City and the surrounds, etc. I personally like the Kerry Hotel for the great gym it has, but since this is the Hyatt forum I would go for the Park Hyatt. The area around the Park Hyatt is a little sterile, but it's convenient enough. The Grand Hyatt looks like it's in need of a renovation, but it is (almost) walking distance to Tiananmen Square.

Another three nights in Shanghai. I would stick with either the Hyatt at the Bund or the Andaz. The Andaz is great for the internet, where it's unblocked and you get access to Facebook and the likes. The gym isn't great at the Andaz, but it does have a beautiful pool. The PH and GH Shanghai are both in Pudong in the business district, which is dead quiet on weekends.

Lijiang is a pretty resort town, but the Grand Hyatt there is new and I've never stayed there before. To go OT a little, I greatly enjoyed my stay at the Banyan Tree Lijiang, which is all villas and has a great view of the snowcapped Jade Dragon Mountain.

Other places you can consider where there's also a Hyatt include Dalian, which I count as one of my favourite cities in China. There's also a Hyatt Regency in Hangzhou, which is just a couple hours away from Shanghai.

Remember western food generally isn't great in all the mainland cities, even at international hotels. I'm Asian so I can go with Chinese food for days, but I generally steer clear of western food except in Hong Kong and a few places in Shanghai.

You might also want to download and install the Astrill VPN if you won't be roaming on data in China. The number of sites China blocks can be very frustrating. An alternative is to buy a SIM card in HK that will allow you to roam in China. Google "CSL data roaming prepaid card $198". You then get unfettered access to the internet when in China.