Day trips by train from Lyon

Beaune comes to mind right off the bat. There's also Annecy. And Avignon. Many options -- if you're only staying in Lyon for 3 nights, that gives you only 2 full days so you'd be spending 1 day enjoying Lyon and the other day doing the day trip to the destination of your choice.

Of course, it also depends where you'll already be spending the other 11 days of your time in France.

Vienne is very close, a 27 minute train ride, and filled with Roman ruins. This was an important port city in Gallo-Roman period. Across the Rhone is an excellent Gallo-Roman museum.

There's a good chance you may find you need all that time in Lyon.

Just to add, we are arriving Lyon via train from Avignon.

Annecy is a bit far from Lyon for a day trip, in my opinion.
Closer to Lyon, besides Vienne, there is Pérouges, a lovely hilltop village, accessible by train if you are able to walk a bit less than a mile each way from/to the station.
If you are into religious architecture, the Royal Monastery of Brou near Bourg en Bresse is also worth a mention.
But for three nights, there is plenty in Lyon already, and if you really feel that you must leave Lyon, then Vienne would be my priority (feasible over 1/2 a day).

I second the suggestion of Vienne.

It depends on your interests. I lived and worked in Lyon for a few years and, assuming you're interested in Roman history, I would agree that Vienne is a good choice for a short hop out of Lyon. Plenty to see and do there.

But, in my opinion, there is plenty to see and do in Lyon to occupy your time for such a short stay. After living there for a time, I have many things on my list to see locally that I still need to do.

And, if Roman ruins aren't your cup of tea, I agree with Balso that Pérouges, a hilltop medieval town accessible from the stop at Meximieux, would be worth a visit.

It depends on your interests as mentioned, but with 3 nights in Lyon I would not plan any day trips if it was my vacation.

If you’re a pinot noir drinker go to Beaune (1h 45m) by direct train.

In the process of planning our trip to France, and I think it is easy to fill 3 full days in Lyon. I wouldn't leave to go somewhere nearby (and use up that time) when you are already in Lyon, and there is so much to do right there. Personally of our 3 week trip in France (touring just this regional area, not all of France), I still put in 4 full days in Lyon, to really have a chance to see all there is there.

Thanks everyone for the recommendations.