There is an excellent map of the Underground available online. I can
change to the District line at Acton Town, Hammersmith, Baron's Court,
or Earl's Court. I have to be sure to get on a train bound for Edgware
Road.

There is cross platform interchange between District and Piccadilly Lines at
Hammersmith and Barons Court, after which the Piccadilly dives underground,
which makes those stations particularly convenient for changing between the
lines without use of stairs, lifts or escalators. However the District Line
services towards Edgware Road operate from Wimbledon via Earls Court so
you'd have to change again at Earls Court (it would be either the same
platform or cross platform). You'd have to weigh up the additional change
against having to come up the escalators and stairs from the Piccadilly
Line.

Then I change again at Notting Hill gate to the Central line, and
get off at Queensway, which is closest to the Byron on Queensborough
Terrace. Or, if I'm feeling adventurous, I could just take the Piccadilly
line all the way to Holborn, then back west to Queensway.

I defer to those who know the stations and the area, but you might want to
consider Bayswater as an option (also on the line to Edgware Road) as I
believe they are only a couple of hundred yards apart. Though Queensway may
possibly be more convenient for the hotel once you are above ground you
might find that is largely cancelled out by the distance to walk between the
District and Central Line at Notting Hill Gate.

G.