John Ray wrote:
I was on a number 17 bus the other day, destination Archway. As we
passed by St. Paul's Cathedral a number 4 bus, also destination
Archway, was heading in the opposite direction. I wonder how many
other places are there where one can catch a bus to the same
destination from either side of the road?

The bus's destination, or yours? To get to Stockley Park from Hayes
and Harlington you can take the U5 or the 350 in opposite directions,
thought the buses don't terminate there. At 8:30 am it is fun to see
streams of people who work in Stockley Park dashing
across the road in the path of a U5 which has turned up first (and
also in the path of any other traffic that happens
that way)

However to get to Uxbridge from Stockley Park you can take the U5 or
the A10 in opposite directions, and both buses do terminate there.
Though the U5 would be a bad idea (as would the 4 in your case)

The road they run on has parked cars on both sides, which doesn't leave room for buses to pass, so all the buses travel east to west on it

This doesn't necessarily produce what the OP wanted, though from the
spider map it does look like the 114 and H9 can be used to get to
Northwick Park from either side of the road at South Harrow.