The London Tube Map is renowned for being misleading about the physical distance (walking distance) between different tube stops. Within central London (Zone 1) its often quicker to walk.
You can see walking distances between tubes stops below. (Use this link to see a big version of the image – London Tube Walking Distances Map)
Alternatively, this Map shows which tube stations are less than 500m apart (400m = approx 1/4 of a mile).
The Soho/West End area is one of my favorite areas of central London to just walk around. I’m a theatre nut (not a mispelling of “theater,” that’s how they spell it in London!). The “West End” theatres are the equivalent of New York’s Broadway. Unlike Broadway. the theatres are not located along just one street, they’re dotted around the neighborhood. A favorite travel activity of mine is to research which TV stars are currently doing plays in London (there are usually at least a few doing this during their breaks between movies and TV shows). I’ve seen US actors like Stockard Channing (from Grease/the West Wing) and Christian Slater. In terms of homegrown British talent, my favorite British musical theatre star is Kerry Ellis who played Elphaba in Wicked in both the West End and then on Broadway. Search theatre and hotel London before you go to see what is currently playing. I recommend making seeing Wicked your top choice if you’ve never seen it before. It’s amazing and I’m yet to meet anyone who hasn’t liked it. Whatever is playing at The Southwark Playhouse is also usually a good choice for a more intimate theatre experience.