Together with last minute flights, last minute hotels are big business nowadays. The idea is that you take a room that would otherwise be empty (often because of cancellations), and in return you get a steep discount. However, as ever, its a case of buyer beware.
It can be a very common experience to arrive in a hotel and find that theres actually no-one in it who didnt come on a last-minute travel deal. This is either because the prices the hotel is trying to charge normal customers are too high, or because its a terrible hotel. To avoid these places, check whether the hotel you find a last-minute deal on is otherwise fully-booked or at least busy if not, you should probably stay away.
Even in good hotels, though, you might find yourself stuck with the one bad room that they havent been able to shift the one that smells funny, or has a view of a brick wall outside the window. While this isnt generally so terrible, you should at least prepare yourself for this possibility.
Its also quite likely though not inevitable that the cheaper hotels will be nowhere near the city centre, leaving you to commute by public transport each day if you want to see the...