I plan to be in London for 3 days in the spring ...

I will try making a short list of the highlights during one of your nights try getting tickets for a musical or any other good show that is on.

Day 1:

Buckingham Palace

Parliament

Big Ben

Try getting on the "London Eye" for a good view of the city and the river or sign up for a bus tour.

Westminster Abbey

 Day 2:

St. Paul's Cathedral

St. Martin-In-The-Field and the Tate Gallery

Harrods

Day 3:

Oxford and Regent Streets-shopping.

Piccadilly Circus

London Tower

Jewel Tower

Hope I helped , make sure you add a visit to a local pub and of course street food. 

I was more referring to cheap junk food in my case Fish Chips is my favorite, but you can still find some Chinese stuff. You should also try the Mildreds vegetarian eatery look it up great place.

Enjoy. 

Patrick's answer is very comprehensive and its hard to add much to it - but its a very heavy schedule. Don't forget to build in some time just to sit in a pub or street cafe and take in the view !

Enjoy your trip to London