SteveWBT said Beijing, Xi'an, etc "are great, but not that different from those in the rest of the world."
I can't help but say he is absolutely wrong and that if you have never been to China, going that route would be the best. There is a wealth of cultural history dating back thousands of years in those cities.
His suggestions for other places to go are excellent, however, but I can not recommend all of them for a first-time visitor because of how far away most of them are (aside from Datong's Hanging Monastery, which is a short 6 hour train ride from Beijing and also has the breathtaking Yungang Grottoes - a must-see, IMO).
For travelers who do wish to go further west - maybe those who did the Beijing-Xi'an-Shanghai trip their first go-around and are now in China a second time - I can't help but recommend visiting these cities:
Dunhuang - Mogao Caves (one of the Three Great Grottoes of China, others including Longmen and Yungang Grottoes), Mingshashan (a desert with an oasis, ruins of Han dynasty (2000+ years old) Great Wall, etc
Jiayuguan - the end (or beginning) of the Great Wall in the west with the 'Greatest Fortress Under Heaven', along with the first tower of the Great Wall and the beautiful (but short) Overhanging Great Wall.
Tianshui - SteveWBT mentioned it, but the Maijishan Grottoes here are pretty beautiful and worth a daytrip.
Yinchuan - the city itself is a huge sprawling mess, but all the treasures lie outside not too far. Go to the Western Xia Tombs, the Great Wall (which is a very different experience from the GW in Beijing), climb mountains at Gunzhongkou, see ancient rock art from thousands of years ago at Suyukou and more. I really believe this city is one of China's best kept secrets because no one ever talks about it but there is so much history and beauty here.
Lanzhou - this is really more of a stop for foodies, imo, as most of the sights here aren't all that amazing. Lanzhou is famous all over China for its Lanzhou pulled noodles (lanzhou lamian). There is also the Mother River statue, the Journey to the West statues, and Zhongshan Bridge, all within walking distance of each other near the Yellow River.
Xiahe - now this is the most interesting town I've ever been to in China, and that's saying something. It's a four hour bus ride from Lanzhou (no train stations here) to this ethnically Tibetan area. The Labrang Temple is here, one of the most important temples of Tibetan Buddhism. Just watching daily life of the locals here is satisfying enough - ethnic Tibetans crawling on the ground, walking around stupas 100 times, spinning prayer wheels, etc is just fascinating. That's not even to mention the Buddhist monks in the temple and the outlying grasslands. Thanks to its remote location, it's not a very popular place with tourists which makes it all the better. Highly recommended.
Xining - after living among Tibetans for a few days, go to Xining and live among the Hui minority - Chinese Muslims. There's the Great Mosque in the city center which makes for a great place for people watching. Outside the city is the Ta'er monastery, another Tibetan Buddhist monastery which is famous for its yak butter sculptures. The birthplace of the current Dalai Lama is also a couple hours bus ride outside of Xining.
I could go on and on about China but what I suggested, I believe, would make a perfect returner's trip to China. Go west, young man!
I've been living in China for three years now, if anyone has any questions I wouldn't mind answering (my speciality is more northern though, as the furthest south I've ever gone has only been Nanjing).
China is an absolutely massive, massive country. You could stay here for months and still have so much left to see.