We only have 2 nights in London after tour, (2 shows booked!). As seniors, prefer a reasonably quiet hotel within one block of the Piccadilly line. We arrive at Paddington, leaving from Heathrow. Budget moderate (300 per night?) but flexible. Very much appreciate your time and thoughts.
Even with specific hotel recommendations in mind I always start with a site like Booking.com to see what is in the neighborhood and compare prices. Once you view a hotel, when you click show it on the map it will give you the prices for all nearby hotels for comparison.
In March I stayed at The Bailey's Hotel across from the Gloucester Road Underground Station with the Piccadilly, District and Central Lines. Classic double room was great for 1 person. I would book a larger double if it in your budget for a couple. Comfortable, quiet, great staff and good in room amenities.
Premier Inns are not on Booking.com but are a reliable and reasonable chain with at least one hotel at Piccadilly itself - handy for your shows.
www.premierinn.com
There are a number of hotels by the Gloucester Road tube stop that should be in your price range. We’ve stayed at four different ones.
We stayed at the hub by Premier Inn London Covent Garden, just steps from Trafalgar Square and is near the theaters. It is about 0.1 miles from the Leicester Square Station on the Piccadilly line and other tube stations are in the vicinity. This may not be what you're looking for since the hub locations have smallish rooms. However they are an affordable place to stay, have several storage shelves, and have a reasonably-sized bathroom.
I like to stay on that line, too. It is good for Heathrow and theaters.
I agree with those who suggested staying near the Gloucester Road tube stop. You can be one minute from the station with handy restaurants and shops. I stayed at The Millenium, but 6 years ago, so am not current with that large hotel.
For a higher budget, South Kensington is a good tube stop with great museum access.
I'll second The Bailey's--I have stayed there 3 times (out of 6 visits to London), last was in August 2024, and it has consistently been a wonderful hotel experience in every way, and is perfectly located for the Gloucester Rd Underground, with shops and restaurants right there. I always choose the biggest room that suits my budget, usually a Deluxe Double.