For a first timer Beijing Xi'An and Shanghai are pretty standard and can be covered over 2 weeks. You could also substitute Yangshuo instead of Xi'An is you like nature and landscape.
The language barrier is less an issue than you think. Beijing and Shanghai are big international cities. Xi'An and Yangshuo gets tons of tourists every year. I would guess that 95% of tourists who go to China do not go on a tour.
HK in a way is similar to Shanghai in the sense that it is a big business city with lots of skyscrapers. If I was to add a place it would be Yangshuo instead as it is something "different". But I don't know you or your interest nor how much time you have.

HK is a fabulous place and a good starting place--no visa required for usa folks..

expensive visa req. for the rest of china, except macau..

beijing, xian and shanghai are all very popular..

how much you can visit often depends on how much time and $$ you have.

language can be a problem in other areas.

you can easily do a trip on your own however

<<<Unlike Europe the language barrier seems to require a guided tour. >>>

Definitely not!

I went on my own to Beijing, Xi'an and Shanghai and loved it. A tour wasn't needed and the language barrier wasn't much of a barrier. The main issues I ran into was trying to tell the taxi driver that I wanted to go to the Longmen Caves (a horrible sketch and the fact that it was the main tourist attraction in the area worked) and when I tried to find tampons (that one was pretty hilarious actually).

My trick was to print out a few things in English and Chinese characters ahead of time. The addresses for my hotels, the main tourist attractions in Beijing, etc. Most menus had English translations and/or picture and most people I dealt with spoke at least very basic English. Charades can actually be kind of hilarious and fun, and if you have a smartphone you can always pull up translations on the go. Also, someone at the front desk always spoke English and was happy to write out anything I needed if I wanted to take a taxi. I simply showed the writing to the taxi driver and off we went.

I liked not being in a tour group because I was more approachable. People stopped to help me or talk to me if they knew a tiny bit of English. An older couple pulled me into their morning exercises in Shanghai. I had time to just wander about where I wanted, to take time here or hurry through there. I spent most of a day in the Forbidden City but little time in the Summer Palace. In a group I wouldn't have had that option. The subway and taxis were extremely easy to use and people were always happy to point me in the right direction. Simply learn hello, please, thank you, yes/no and how mcuh and you'll be fine if you choose to go on your own.

I would go back to Beijing in a heart beat.

Read through some trip reports to get an idea of what other people have done, what worked for them and what sounds like something you think you might enjoy.

I just want to echo the sentiment that there is no need for a guided tour in China. If you can travel in Europe on your own, you can travel in China on your own.

Do your homework and you'll have no problem traveling on your own, in the large cities, people are warm and willing to help especially after the 2008 Olympic Games and the 2010 World Expo.

I agree with the folks who say there is no need for a guided tour. Absolutely none. Travelling on your own is so much more rewarding. Guided tours usually don't allow you to linger long enough to truly absorb a place. Buy a Mandarin phrasebook and you will be set. The people are so helpful and once you can get past the spitting, staring and slurping of food then you will really see this.

The big cities are well documented and where you go here depends on personal preference. Beijing, X'ain, Shanghai and HK are all excellent places.

One bit of off the beaten track advice I would give you is the following:
If you are travelling from Shanghai to HK overland then there are two very worthwhile jumping off points en-route. One is Wuyuan and the, more specifically, the postal villages around Wuyuan. Truly beautiful, with some excellent walking options. Secondly, the roundhouses (hakka / tolou) in Yongding County are also very scenic and historic. Overnighting in one is an experience to say the least!!

Enjoy!!

Thanks for your comments. That is encouraging that you have done it on your own. I have helped a lot of people who thought the same about guided tours in Europe. I tell them they will do just fine and so far we haven't lost anyone to the "unfamiliar monster".

Thinking of a similar trip in the fall and look forward to seeing your itinerary as it progresses. We also would like to avoid a tour if possible.

If you want help but don't wish to join a tour then hire a guide. At 400RMB per day they are quite cheap (cheaper in smaller cities).

>>Unlike Europe the language barrier seems to require a guided tour. <<

If you stay within the main city then it shouldn't be too much of a hassle to get to where you want to go. Beijing has a fantastic subway system. It can get tricky when you want to venture outside of the city on your own though, depending on how adventurous you are. I remember being anxious taking public transportation to visit the Mutianyu section of the Great Wall; Inside the bus, the destinations were scrolling across a screen at the front, but they were all in Chinese characters. I was constantly comparing the onscreen characters with those in the guide book and prayed that I got off at the correct stop, LOL.

If I do go back I think I would either hire a guide or work with my hotel to hire a driver and car for a day.