Renting a Car in Lyon

Go to Annecy.

I think there's a lot going on in Lyon on Sunday. Tuesday many attractions are closed, though of course it is a big city and does not shut down.

If your question is whether to get a car and drive into the countryside versus going into Lyon, I'd say go to Lyon by public transport. There will be plenty to do. And you don't need (or even want) a car there.

I'm curious what "tourist places" you have been led to believe would be closed on Sunday.

Parc de la Tête d'Or?
Vieux Lyon?
Basilica de Notre-Dame de Fourvière?
Roman ruins?
Musée gallo-romain de Lyon?
Les Halles de Lyon Paul Bocuse?
Marché Saint-Antoine Célestins?
Place Bellecour?
Musée des Beaux-Arts de Lyon?
Centre d'Histoire de la Résistance et de la Déportation?
Musée Lumière?

I ask, you should understand, because all of those are open on Sundays. Now, if your idea of tourist places includes shopping malls and retail stores, then, yes, most will be closed (unless you want to visit the predominately Middle Eastern grocers and retailers in the Guillotière area of Lyon).

If you want to get out of town, I would suggest visiting Pérouges or Vienne. With more driving, you can hit Grenoble or Annecy or even Chamonix, which in my view is a much better place to visit than Annecy. Heck, even Geneva is a day trip from Lyon, if you want to check it out.