I’m not sure how British Airways can get these deals, but they seem to be legit and probably worth checking out: Special Offer hotels from British Airways Holidays
With these deals you can pay for 2 or 3 nights at a nice hotel, and then get a free night included. Amazingly enough, many of the hotels seem to be quite reasonably priced to begin with, so getting a free night makes a good deal even better.
Speaking of nice hotels, there are some nice hotels in Nice, and one here called the Beau Rivage is a 4-star hotel starting at £75 per person per night, with a 4th night free. Sure, there are cheaper hotels in Nice, but this is a 4-star place during the summer in the South of France! If your budget is a little lower, then you might be interested in a 2-star hotel in Paris where the 3rd night is free and prices start at £37 per person per night. That’s 3 nights for two people in Paris for under £150 total. British Airways, have you made a pact with the devil?
