Dinner in Paris on my own

For a classic bistrot meal e.g. beouf bourguignon or duck confit or steak try Chez Dumonet Josephine. Get reservations.
http://www.zagat.com/r/restaurant-josephine-chez-dumonet-paris?gclid=COmrl6CE8L0CFUVgMgodiy4Agg

for an elegant multi course meal beautifully presented Le Cottage Marcadet near the Lamarck Caulaincourt metro in Montmartre -- also get reservations.
http://www.cottagemarcadet.com

For a great little place near the Tuilleries try La Cordonnerie. Small, one chef place. Get reservations. Try their grilled fois gras with cocoa sauce if it is on the menu. http://www.restaurantlacordonnerie.com

for an inexpensive but excellent Breton crepe, try Joselin on Rue Montparnasse near Gare Montparnasse.
http://www.timeout.com/paris/en/restaurants/josselin

Or just let your hotel recommend something nearby. The French love food; you see people dining alone all the time; it is perfectly fine anywhere.

There are hundreds, if not thousands, of nice places to eat in Paris, and some of them are near your hotel, wherever it is! You could ask at the desk, or just take a look around the neighborhood. Menus are posted in front of every restaurant so you'll know what you can get and what prices are like. If you don't know enough French, you'll probably find places with bilingual menus, which means waiters will speak enough English to help you figure things out. Those places may have other American tourists eating there, but so what? It's just one dinner. Have fun, and think of the in-depth knowledge you'll be able to display to your fellow-travelers when you all get together the next evening! ;)

Ann, Where is your hotel located? I have favorite restos in many parts of Paris (serving steak/frite, Moroccan food, cassoulet, beef bourguignon, etc., all at reasonable prices) and will be glad to share with you.