Vieux Lyon is quite touristy, with lots of small tourist-oriented shops, interspersed with a few that aren't geared toward the tourist trade. It's also very crowded in the summer.
The Presqu'île is a bit more "normal" (that is, it has lots of restaurants, shops, and services that residents of Lyon use) but still is convenient to transit, museums, lots of hotels and sights such as Vieux Lyon. Don't get me wrong: there certainly are tourist-centric areas of the Presqu'île (such as restaurant row on rue Mercière), but in my opinion, you generally will find a better grade of dining and shopping between the Rhône and the Saône than in Vieux Lyon.
Another area of Lyon to consider is Croix-Rousse. It's got a different feel than the rest of town and also has some good restaurants and shopping. You can get there easily by bus or Metro (or by walking, if you like hills and stairs).