Is that a true 4 days or does it include your arrival and departure? When are you going? This summer? Fall?
Asking because Summer is a mad house and tickets to the Tower, the Abbey and even St Paul's should be booked in advance. You should also see if you can qualify for the 2 for 1 deal by reversing the itinerary I've suggested below and taking a train on Day 1 to either Bath or Windsor. https://www.daysoutguide.co.uk/2for1-london
Day 1:
Tower of London. Opens at 9am. Get there a minimum of a 1/2 hour earlier to get your tickets and snap images of the venerable Tower Bridge. Once through the gate go past the Ravens to the Crown Jewels exhibit. Then see the rest of the Tower. Beefeater tours always a plus. Very knowledgeable.
After visiting Tower start walking towards The Gherkin. Once you see it (or Google it) you'll know which skyscraper I'm referencing. Nearby is the futuristic LLoyds Bank building and it butts up against the historic (14th century) glass covered Leadenhall Market for lunch. Quite the architectural dichotomy. From the Tower of London to Leadenhall is a 15-20 minute stroll. Have lunch there. If Harry Potter fans look for the entrance to the Leaky Caldron.
From there its another 20 minute walk to St Paul's Cathedral. Expensive admission. Now it's mid afternoon so time for a pint or late lunch at the art deco Blackfriar Pub which is 10 minutes from St Pauls. Right across the road is the Blackfriar train and underground station to get you back to your accommodation or if still up to exploring you could walk along the Thames path as the sun goes down and the city lights go on.
Day 2
After confirming that there aren't any special events happening at Westminster Abbey. Tube to Westminster. Exit and wander about Parliament Square. Consider a Verger's Tour of the Abbey. Worth the money IMHO. After seeing the Abbey walk across the road to Birdcage Walk and meander through St James Park up to Buckingham Palace. Double check the timing of the Changing of the Guard and try to avoid it as crowds can be massive and unless right in front you won't see squat.
After seeing the Palace walk down The Mall passing the Clarence House (behind gates) heading towards Admiralty Arch, walk through it and onto Trafalgar Square. Have lunch in the Crypt at St Martins of the Fields or at Punjab at the adjacent Covent Garden. Afterwards visit the free National Gallery.
Day 3
Train to Bath. Explore Bath. Train back to London.
Day 4
Train to Windsor. Visit the castle. return to London.
GREAT city. Enjoy your time there.