I've been to every province in China (Including Taiwan) and lived in Jilin for many years so here are my thoughts (For what they're worth).
Jilin: As others have said; eastern Jilin is the most interesting part of the province. Changchun is OK for a day or two (If you like architecture). But the east, along the North Korean border, is where the history and culture are. The HSR has made Yanji a lot more accessible (And, from it, the rest of Yanbian Korean "Autonomous" Zone) but Tonghua, the hub for visiting Ji'an and other Koguryo archeological sites, still hasn't been connected (Although the station was built 2+ years ago) so still takes time to get to.
Shandong: Has Qufu, which is really nice in the early summer, Tai'an for Taishan, Ji'nan for....errrr...hot pools? And, of course, Qingdao; for a little touch of Germany. It also has Weihai that has some lovely beaches and a little touch of England on Liugong Dao. It also has dozens of wrecks lying nearby from previous useless Chinese navies. I'm not sure if you can dive them but would be interested to find out..
Fujian: Many people like Quanzhou (I'm less enamoured). But the Fujian interior is beautiful. The Tolou are interesting, Fujian natives are friendly and Xiamen is, certainly, worth a look.
Xinjiang: You could spend all of your time in Xinjiang. Amazing place. But skip Urumchi. It's rubbish (Although many people say it has a great museum). Kasgar is a must (Before it gets totally ruined... If it hasn't already). Turpan and Hotan should also be on everyone's list.
Inner Mongolia: Is patchy. There is only so much grassland I can view before I start to get bored, There are some interesting towns (Chifeng, for example) and there are some little gems that nobody has ever heard of. But the entire province isn't really set up to cater for foreign tourists and many of the sites that a foreigner may want to visit (Xanadu, for example) aren't worth the considerable effort.
Chongqing: Good for hot food. There are 1 or 2 things to see around the town and Dazu is worth a day-trip. The place is a swine to walk around though; built, as it is, in a very steep valley.
Ningxia: Is boring. Granted! I've only ever been to Yinchuan (And Yinchuan is boring) but I don't know of anything else that may attract a visitor to Ningxia. I have tentative plans to visit Zhongwei at some stage in the not-too-distant future. But I'm just planning that visit as I've never been there and there is a convenient night-train out of Beijing. There's nothing that particularly draws me there.
Jiangxi: Is my least favourite Chinese province. Some of the little villages near Huangshan are worth a look. But Nanchang is rubbish and Jiangxi people tend to be seriously unfriendly to boot.
Your biggest problem will be linking everything in. I think, if I were you, I would start in Xinjiang, move across through Inner Mongolia and Ningxia to Jilin, then head down to Shandong, hop over to Jiangxi, Fujian and, finally, on to Chongqing.
P.S. There are 34 provinces, 'autonomous" regions and Special Administrative regions if you include Tibet, Hong Kong, Macau and Taiwan.