Day trips from Lyon
 

Will be there 4 nights so thinking two days to see the city will probably do it. Good day trips from there? Nothing too far, maybe 4-6 hours travel time and sight seeing max.

Annecy is a 2 hour train ride away. Beautiful city, and can rent bikes and ride along the lake and explore the area.

Geneva is less than 2 hours away by train

Lyon-Part Dieu to Paris Gare de Lyon in just shy of 2 hours via TGV.

If you'll have a car, head for some of the wine villages.

Dijon is easy by train and worth a visit if you've never been there, or you could take a train in the other direction to Avignon, although a day might not be enough time there, depending on how interested you are in church history.

I'd suggest the following:

Annecy
Geneva
Aix-les-bains
Megeve / surrounding area (might be a bit far though)
Chambery

Annecy is also definitely my #1 reco.

+1 for annecy for sightseeing

If you are a foodie/winesseur, Bourg-en-bresse or Macon might be an idea.