Am planning to split 6-7 days between Lyon and Dijon.

If I will be arriving in Lyon on a Saturday, how many days should I allocate there before heading up to Dijon?

While in Dijon, I also plan to make a day trip to Beaune.

It all depends on your interests. You need to be a tad more specific about what turns you on. If you're going to Beaune, then it's probably wine.

Lyon has some great restaurants and is a pretty city. Dijon is smaller, with a definitely different atmosphere. Dijon also has very good cuisine, holding its annual Gastronomic Fair.

My first trip to Dijon I got to see a bar fight, which the normal tourist never sees. That is something I've never seen again in my 40+ trips to Europe.

We spent 5 days in Lyon and didn't see all there was to see. Several excellent museums, churches, silk tours river cruises and great food!Spent 1 day in each of Dijon and Beaunee and felt we covered most of it

You should definitely spend at least 4 days in Lyon as the city is much bigger than Dijon and there is much more to see and do there.