Lyon isn't a bad place to have a car if you want one, or will need it afterwards. There are at least a few good day trip options from Lyon.
In terms of best area to stay my favorites:
The old city center between the funicular and the river is the best area. Most of the sights are close and there are lots of restaurant choices within walking distance. The funicular marks the start of a steep hill. The hill is roughly parallel to the river, so look in the band along the river and avoid staying on the steep part (from personal experience).
If you can't find something there, directly across the river from that area (between the rivers) would be my second choice.