I would suggest either County Hall or the Renaissance Chancery Court.
County Hall is located right on the Thames River directly across from Big Ben. A river view room upgrade would cost $30/night, well worth it.
County Hall is minutes away from Big Ben and Parliament. Closest tube station is Westminster ( Circle and District Lines ).
Chancery is on High Holborn St. near the west end, just minutes from the theater district, Soho, and the British Museum. Nearest tube is Holborn ( Central and Piccadilly Lines )
County Hall with Big Ben out the window was wonderful. But I preferred Chancery because it had just a bit more warmth and ambiance. But both hotels are first rate Marriott properties.
Be warned, London is expense and breakfasts at the hotels run inexcess of $25 for a hot buffet.
Have a great time.
Barry