I would sure try to hit JJ Fox if possible. That is where the Pipe Club Of London meets. It's one of my favorite places in London. But looking at the address (19 St James's Street, London) compared to your hotel, it is a bit of trek to get there and they close at regular business hours. It might be tight to get there.
In these major cities it is tempting to take public transportation, but in this case, I'd highly recommend you break for one of London's famous black taxi's. It will save you the energy of a day's work going and coming. Boarding one of those ancient wooden-step escalators in the Underground for the thirty-fifth time, my late wife and I just broke into spontaneous gales of laughter at the repetitious monotony of the thing. After that we still rode the Underground but took some cabs too.
Do not miss Fox's, they are great people. Great history in an interesting part of London for manly pursuits. St. James is also home to Geo. Trumperer, Taylor of Old Bond Street for shaving, Tricker's and Church's for brogues, Pinks of Jermyn St....and of course, the Clubs.
Dunhill is near Davidoff - just walk past Lock and Co, same side on St. James’s.
There is also a small tobacconist in Covent Garden. Quite charming. I bought a B42 Standard and a pouch of one of their mixtures. Came home with a broken-in pipe and almost no mixture left :puffpipe: