I second the Audley and the Grenadier.....both have completely different atmosphere.....good food...we have enjoyed the Grenadier several times...would also suggest Old Bank of England on Fleet Street, simply for its architecture and rather grand decor...food also good, but feels more like a restaurant for business men/women at lunch. Actually I think that is what it is. We have enjoyed it nonetheless. Sometimes it's just fun to wander into whatever pub is nearby. There will be a different experience everwhere.Enjoy it!
p.s. Swanhunter's link is excellent. Will give lots of insight.