The Trafalgar Square in central London is one of the busiest public space where tourist come and go. This is one of the landmark in London and events are also being held there from time to time. One can just sit on the bench and rest after touring around.
If you are a traveler in London, it would nice if you can stay at the nearby hotels so it would be more accessible to various tourist destinations but this can be very costly. If you are in a tight budget, you can have some apartment instead instead of staying in a hotel. Going in group can also share in accommodation.
Hotels and other accommodations around Trafalgar Square:
The Trafalgar Hotel
Citadines Trafalgar Square Apartments
Broad Court Apartments
Covent Garden Studio Apartment
There are other cheap accommodations you can find, just plan it advance and really search for a good deal for your stay.