There are a lot of good places in and around Beaune, from the high end and sophisticated (Lameloise was mentioned, as was Le Montrachet in Puligny), to up and coming creative chefs (like Stephane Leger in Chassagne at Le Chassagne), to more relaxed but delicious places like Ma Cuisine. What type of place are you looking for? Do you wish to walk or are you up for a drive?
We definitely plan on doing Ma Cusine ..but beyond that we are still planning.
I am currently debating to whether to rent a car the three days we are in Beaune. We are doing a tour through Taste Burgundy one of the days and wonder would a car be worth it the remaining full day we have? We were thinking one of the evenings doing dinner at Lameloise. Is a taxi service a reliable option in this case?
Doing a wine trail crawl between Beaune and Dijon is a delight. Having your own car is a plus. Besides the important domaines (for which you should probably have an introduction or at least the intent to do some rather serious buying) there is Fromagerie Gaugry, one of the last producers of raw milk Epoisses http://www.gaugryfromager.com/spip.php?article21 , the very interesting if Disneyland-esque factory museum , the Cassissium, at Nuit St. George where you will learn all about (extensive tour) and taste cassis and marc. http://www.cassissium.fr/ and, some 15km off the main road you find the Abbey de Citeaux where you can wordlessly buy the famous cheese by the same name from a monk sworn to a life of silence. http://www.fromages.com/cheese_library_detail.php?id_fromage=200 ; http://www.sacred-destinations.com/fr...
Rent the car! It will give you so much freedom and there are many great things to see even if they aren't "sights". Driving there is easy and there is pleanty of parking (except during big festivals).
Taxis are available, but spotty and rental cars are inexpensive.
Agree with mangeur on the wine drive between Beaune and Dijon, though I'd skip the Cassissium unless you have kids.
I can also highly recommend a day tour with Sarah Bird of Detours in France. This would get you out of town without a car. She is a Canadian who is married to a local and has lived in the area for 20+ years. Very knowledgable and brings the history alive without boring you to death. I'm cheap and like to travel independently, but still find that we do at least one tour with her every time we're there. www.detours-in-france.com
Here are two recent threads with some of my favortie restaurant recommendations in/around Beaune:
Another two we recently discovered are:
Via Mokis - great food and wine - www.viamokis.com/gb/home.html
La Cabotte in Nuits St. George - cozy and really good food - www.resto.fr/lacabotte/
Also - personally I wasn't impressed with Loiseau des Vignes the Bernard Loiseau restaurant in Beaune. It was good, but not great. Pleanty better around. I've heard that the Saulieu restaurant is his focus and much the better for it.
Definately agree with Domaine Lucien Jacob recommended by ChefJune. The wife is English and the husband French. He also likes to try his hand at some very interesting "art" made from used barrels.
Relais Bernard Loiseau in Saulieu is not a long drive from Beaune, and is well worth the detour. There is much to taste between Beaune and Saulieu, in any case.
Especially recommend a stop at Domaine Lucien Jacob for a tasting of their excellent Cassis, Framboise and Mure. I have had none better anywhere. Though they are available in US, they are frequently hard to find, and the tasting is a very lovely experience.