You will have a good time!
I was born and raised in Beijing, and I think you will have a good time there. There is just so much to do! I don't know when are you planning to go there, but usually winter and summer are not the best time in my opinion because of the weather.
Not many people speak English there, but with the Olympics in 2008, I think the taxi drivers were required to take their English lessons, but I doubt the effectiveness of that. So a phrase book or bi-lingual tour book of some sort will be good to have. Normally, you will have better luck with the younger generations, since English is the required course in middle school. But people usually understand more written English than actually speaking it.
For shopping, I suggest you avoid the places where the tours take you. There is a local market call HongQiao, outside the Temple of Heaven in Beijing, that offers good souvieners and unique Chinese stuff. I shop there every time I went back to Beijing. You have to bargain hard, but that's part of the fun, isn't it? To asp's point, bargaining was all done on a calculator.
As far as Shanghai is concerned, I don't think you will need the whole week there in the city. But if you can take some tour to the neighboring city like Suzhou and some little villages, it will be interesting. (I still have to do that myself
Another thought about hiring a local tour guide is to find a local colleage student. They will be more than happy to get an opportunity to practice their English and make some money at the same time, should not be very expensive. I remember myself as a tour guide while in my colleage days
Most likely you will take a cab with your guide, but they can also take you to experience the city, by bus, subways or maybe even rent a bike if the weather is not too bad.
If you haven't already, I would recommend you to get one of those Lonely Planet tour book on Beijing and Shanghai. (I hope they have a Shanghai one.) They are really good. I remember taking my English speaking friends touring around the city who had this guide and I have to say, it is really good. Even for a local like me, I get to see and learn interesting things I would not have done without it.
Enjoy your trip!