Nice Lunch in STL
If you walk over to the Wine Merchant ...just across the cul de sac from the Ritz...you can pick up a great bottle of wine (VERY reasonable prices and GREAT staff). They also have the most amazing cheese counter...full of beautiful cheeses, meats, olives...they also have a fresh baguettes brought in every morning. There's not spot to eat it there but if you would like a light lunch in your room...that's the best ticket. Too bad the weather isn't cooperating and you could have had a nice park lunch.
I would also second Pomme Cafe. The walk isn't that far and it's a quaint little spot with a decent wine list...GREAT onion soup and the best fresh croissants in Clayton.
I'm not sure that there will be any place within immediate walking distance that are also open for lunch. The two closest restaurants, Araka and Luciano, would meet your needs, but do not serve lunch on the weekends.
A place that is nearby, Pomme Cafe, may work. It is probably 1 mile away or so (a long walk, but a very short drive). Pomme Cafe is a casual cafe (it has a more formal counterpart Pomme Restaurant next door) with good, french inspired food with an adequate wine list. It is a comfortable place and should provide a good experience.
Obviously, there are also the restaurants within the Ritz that may work as well.
I've never been to the restaurants at the Ritz, but I've been to both Luciano's (this was a couple years ago) and Araka. Honestly, I wouldn't highly recommend either one, but I'm notoriously picky. Luciano's is generally well liked by most and is an upscale Italian restaurant. It's definitely a nice place and we were well taken care of, but I generally don't get too excited about Italian restaurants.
Araka opened in the Fall of 2007 and has generally received good reviews. It is a well designed restaurant and a beautiful space. Unforunately, I found the food only adequate. We had great service and a good time, but it definitely is not a foodie destination. I do think it would work very well for what you are looking for as it has a respectable wine list.
I'd probably recommend Araka over Luciano's. I hope this helps and I hope you have a good experience at wherever you choose.