Gayle,
I assume you would be arriving at Gare de Lyon Part-Dieu. If you're hoping to buy lunch after 1 PM, that could be a bit of a challenge because a lot of restaurants stop serving lunch around 2 or so. If you're looking for dinner, then I can suggest a few places you might want to try.
For fancy spots, Lyon's most expensive neighborhoods are in the 6th arrondissement, north of Gare Part-Dieu (which is in the 3rd). Some places there that are very good are:
Restaurant Pierre Orsi -- probably the fanciest place on this list.
Restaurant les Apothicaires -- also quite good
Le Gourmet de Sèze -- the first Michelin-starred restaurant my wife and I visited after moving to Lyon. I couldn't believe how attentive the service was.
Less expensive and run by a delightful couple (as with many smaller restaurants), with the wife in the front and the husband in the back working the kitchen, is Le Florentin on 7 rue Tronchet, Lyon. That was a short walk from our old apartment and we had many delightful dinners there. No website as far as I can tell, but you should be able to find them on restaurant aggregation sites like The Fork (La Forchette).
A little closer to Part-Dieu would be Brasserie L'Est (click on the "E" for est, or east), one of the Paul Bocuse chain brasseries scattered around Lyon. It's in the old (but beautiful) Brotteaux train station. It's fine. Not the best, but shouldn't disappoint. Look for the little toy train running on a track around the room just beneath the ceiling.
Better, in my opinion, and one of the most beautiful tiled interiors in a restaurant I've ever seen, is Brasserie des Brotteaux, across the (very wide) street from the former Gare de Brotteaux, where L'Est is located.
The latter two are a reasonable walk from Part Dieu, though you could catch a bus or take the Métro (subway) there. The ones in the sixth could be walked to, but you're better off with transit or a taxi.
Hope that helps. There are probably hundreds of restaurants in the area and a lot of good ones I haven't mentioned, but you shouldn't go wrong with the ones noted above.