As a former Lyon resident, I would disagree that Lyon warrants only two days for a visit. It's a large, fascinating city, with a variety of things to do depending on one's interests.
A few things to think about:
A walk from Place Carnot, near the Perrache train station, up rue Victor Hugo to Place Bellecour passes by many interesting shops. Rue de la Charité just to the east is an alternative, but both get you to Bellecour. It's a huge square with a large statue in the middle and there often are events set up within the square. If your daughter has read Le Petit Prince, a short walk SW from Bellecour takes you to the intersection of rue Antoine-de-Saint-Exupéry and rue du Plat. There, above a fairly plain brown wooden door, is a plaque commemorating the birthplace of Saint-Exupery. Return to Bellcour and continue north a short way to Place des Jacobins to see its beautiful fountain and impressive buildings lining the place. A short walk up rue Mercière is a pretty impressive introduction to dozens of restaurants with outside dining. True, many of them cater to the tourist trade, but it's still an interesting sight. Cut east past rue du Président Edouard Herriot over to rue du République and continue north, noticing the fountains and stores. You'll pass the grand Bourse and end up at the opera house. Head west past the Hôtel de Ville to Place Terreaux to see the recently restored fountain by Bartholdi, who also sculpted the Statue of Liberty. Then, duck into the garden in front of the Musée des Beaux Arts to enjoy the peace and quiet (and cool shade if it's warm while you're there). If art is an interest, the museum is definitely worth a visit. And, if you're game, head a short distance northwest to one of the Roman ampitheaters in Lyon, the Ampithéatre des Trois Gaules.
Transport yourself back into the Middle Ages in Vieux Lyon. Visit Cathédrale Saint-Jean-Baptiste and see its incredible astronomical clock dating from the 1600s. Duck into a traboule or two. Take the funicular that ascends Fourvière Hill and visit the ornate, mosaic-filled Basilique Notre-Dame-de-Fourvière, both upstairs and downstairs. Climb up to the roofs to see close up the Saint-Michel statue and to look over cental Lyon. The still-used nearby ampitheatre is worth visiting as is the adjacent Gallo-Roman museum. Descend back to Vieux Lyon via the peaceful, leafy, winding path through the Parc des Hauters.
If you're interested in Lyon's food heritage a couple of things to look into in addition to the city's restaurants are the massive Marché Saint-Antoine stretching along the Saône river, and les Halles de Lyon Paul Bocuse. Just walking through les Halles to see the various shops and products on display is pretty amazing.
If your daughter is interested in flea markets, Les Puces du Canal in the suburb of Villeurbanne (accessible by bus) is pretty cool and you both will see stuff you haven't seen before.
If fabrics are an interest, a visit to the Lyon Musée des Tissus is in order. Before going, help your daughter learn about Hollerith cards and how they were used to load and run computer programs. Then, see a massive loom with its punched cards that tell the loom how to weave the pattern of the fabric -- it's essentially the same technology; separated by centuries.
The huge Parc de la Tête d'Or, Lyon's backyard, packed on warm summer weekend days and quiet most other times. Enjoy the large greenhouses with specimen plants, the free zoo, the rose garden, the classical sculptures, the pond with the War Memorial on the island, and the adjacent Cité Internationale with its modern architecture and sculptures.
If WWII is of interest, th Centre d'Histoire de la Résistance et de la Déportation is a sobering look at Lyon during those trying times.
I'm out of space now, but consider a visit to nearby Pérouges, and see the well-preserved medieval town that was used to film, if I recall correctly, three different Three Musketeers films.
