If you only want to spend little time in museums and a quick overview of all that Lyon has to offer, you should definitely go to the musée de Gadagne in Vieux Lyon. I went there on Sunday with my family and it really gives you a quick (2 hour) summary of every other museum in the city, and even if it doesn't go into too much detail, you can spend quite some time wandering it's halls.
There are audioguides available in almost every language, which makes it accessible also for English speakers and families with children whose English isn't quite good yet. The exhibition begins on the ground level with ancient roman and middle aged times, and slowly winds its way around and up the building to end in the 70'. I found it quite thoughtful that the audioguide mentioned every other museum you can visit to broaden your understanding of a certain subject, and they cross-referenced almost every museum I'd already visited. This made it quite nice for a quick refresher and also a good summary.
After talking quite a bit about Lyon's ancient history, it delves further into the (counter)reformation and also mentions the silk working industry, which I already wrote extensively about in my post about the Maison de Canuts. I found it rather interesting how through the silk industry, a lot of chemical and mechanical factories sprung up and helped Lyon diversify. They also had a few rooms about the French Revolution, which I had heard only about in Paris, so it was wonderful to get another perspective. There were about 30 rooms in total, with some closed for renovation - the building contains another museum (about puppets), but this one is closed for another two weeks while undergoing renovation. The last few rooms talked about the résistance and the social apartments (this is most definitely the wrong word for H.L.M/Gemeindebau) that were built in the 30' and later years, ending on a note about the revolution of 68'.
I liked that they used different forms of media, not only text but also quite a few videos, they also had quite a lot of stuff on display. Certainly I will send everyone who's visiting me to this museum, as it provides a wonderful overview of the whole city!