I'm from the US but currently living in Reims. Here is a good list for you and a link to my blog where I write about food around here: http://thetastysidetolife.blogspot.com/
Grand Cerf- Dying to go here. 33 Euro for a 3 course menu during the week! Looks so beautiful. It’s outside Reims in the country (on the way to Eparnay) so you need a car to get here.
Le Millénaire – In Reims, 1 Michelin Star
Le Foch- In Reims, 1 Michelin Star
Les Crayeres- http://www.lescrayeres.com/lechateau_204.html. The Jardin has the most beautiful patio seating in the summer. Ahhh also go to the expensive brasserie for a drink because its soo cute in their and so French.
Less Expensive Options:
Le Petite Comptoir
Sushi Shop-really good sushi, try the tulip avocado tartare of saumon and try the fois gras roll! http://www.sushishop.fr/fr/accueil#/categorie/maki
Version Original. http://www.vo-reims.fr/ stunning inside. Just discovered this but looks soo great. 15 euro for a salad so a little pricey
Anywhere on Rue des halles or outside in Place de Forum (Edgar Bistroe) on Rue Colbert or anywhere in Place de Forum there is outside sitting which is super cute
* If you can, stay away from eating on Place d’Erlon (just kind of generic, not good French food..)!!
Hope that helps!