You could take the cable car or walk up to the Bastille and enjoy great views on a fine day. Several hikes also start from the Bastille, and I believe there’s also an Acro’branches (go ape) which could be fun.
Vizille chateau is not far away and is worth a visit. It’s reputedly the birthplace of the French Revolution and is set in extensive beautiful grounds with a deer park at the far end.
Activities in the mountains will depend on the weather: if there’s no snow you could hike or bike in the Chartreuse or Vercors mountains. There are several shops in Grenoble that rent bikes. You could also bike along the banks of the Isère.
If there’s already some snow in the mountains, why not try some snowshoeing? Check with the local tourist office before you set out that your proposed route is safe, and that the weather forecast is OK.