You can pick up the bus in front of the Gloucester Rd Tube stop. It heads over to Marble Arch Area as kind of a dispatch area where guides switch and take breaks (recommend the live guide over the headset, as they are generally quite funny), so you can take a quick Tube to Marble Arch as a starting point as well if desired. And yes, they hit all the sites in Central London.

Can't help with eateries close by as I never munch near the hotel.