If you have not spent a lot of time in London, try Duke's Hotel. Small, elegant, expensive (but no worse than any other).
Believe it or not, The Rennaissance Hotel at Heathrow is reasonable (half the price of Duke's) and quite nice.
My walking tour is as follows: Start at Purdey, make way to Boss, Holland, William and Co.; go down Bond St. Look in at Burlington Arcade, down Picadilly to Cordings for shooting clothing, backtrack to St. James St. to visit Swaine Adeney, William Evans, and Beretta Gallery, then down Jermyn St. to look at Edward Green shoes, T and A shirts, etc. then down to Farlows for fishing stuff. In between, lunch at Green's restaurant.
Where Woodward used to be:
Where Greener used to be:
What $600/night gets you in London: