We've been to London several times. The Eurostar train takes you in about 2 hours time from Brussels-Midi station to St Pancras International station in the center of London. We usually try to be in a different area and that allows us to discover new places.
Let's hope that Brexit will not stop us from visiting.
Hotels tend to be very expensive in the big cities, but there is also always a good deal around if you do not mind being a little bit away from the tourist or business areas.
As we take our Brompton bikes on a city trip, that gives us a lot of flexibility when choosing a hotel.
A lot of restaurants have an Early bird menu, if you have dinner before the crowd comes, you get a cheaper price or some additional stuff thrown in.
Get discount tickets for shows on the day of the show on one of the many last minute theatre ticket shops.