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Put together with late hour flights, last minute hotels are big business now. The thought is that you book a room that would otherwise be empty (often because of cancellations), and in return you get a steep discount. Nevertheless, as ever, it's a case of buyer beware.
It can be a really common experience to arrive in a hotel and find that there's actually no-one in it who didn't come on a last-minute travelling deal. This is either because the cost the hotel is trying to billing normal customers are too high, or because it's 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 may find yourself stuck with the one bad room that it haven't been able to shift - the one that smells funny, or has a view of a brick wall outside the window. While this isn't generally so terrible, you should at least prepare yourself for this possible action.
It's likewise quite likely - though not inevitable - that the cheaper hotels will be nowhere near the city centre, allowing you to commute by public transport every day if you want to see the sights, or additional hang around in the suburbs. You should consider the costs of transport prior to you book, as a slightly more expensive hotel that is more central can often save you more than it costs.
A final thing to be aware of is that you can frequently get a good discount by booking a late minute flight and hotel as a package deal across the various agency sites. If you are doing this, though, make certain that you don't let the savings pressure you into taking a bad flight or a bad hotel just for the other half of the deal seems so good.