This is a very highly subjective list based on my own experience and tastes. I’m a budget traveler, so these three choices reflect that fact. Bordeaux restaurants are very reasonably priced for the most part, anyway, so I think you’ll find that you can get wonderful meals for a lot less than you might expect to pay. So here goes - my three budget favorites:
Viandocks - Okay, if you’re a vegetarian, don’t bother reading this - Viandocks is strictly for carnivores. In fact, this restaurant is located in what was once a butcher shop, so that should give you an idea what to expect. Located on the Quai de Paludate, near the train station Gare St. Jean, Viandock serves a variety of grilled meats cooked to perfection. Beef Tartare, Beef Ribs, Tournedos with Foie Gras, Roasted Chicken, and all at prices even students can afford. Three-course meals for around 20 euros.

Les Halles - This small, friendly brasserie is located one block from Les Capucins - the large open-air market from which Les Halles gets its fresh vegetables and meats. A chalkboard menu with a limited, but satisfying selection. The English-speaking manager, David, delights in playfully badgering customers. An intimate, inexpensive neighbourhood favorite. Try the Pork Tenderloin Tournedos with Apricot Sauce or the Roasted Camembert appetizer. Main dishes are under 20 euros.

Le Palatium - I’m a little hesitant to recommend Le Palatium, as they are somewhat inconsistent, but the prices are very reasonable and I find the slightly crowded, boisterous atmosphere strangely attractive. Yes, they serve chips with most meals and they have disappointed at times, but there is something about the vibe and the food that keeps me going back there. Quite inexpensive, and in a convenient location right in the centre of town.

Bordeaux is the perfect weekend getaway for Brits, or for a full holiday - airfares from most London airports are very cheap. A bit of advice: book a room in a hotel near the airport the night before departure, such as one of the Gatwick airport hotel or any of the hotels in Luton, depending on which airport you’re flying from. You’ll arrive at the airport refreshed, on time and ready for your flight to beautiful, romantic Bordeaux.