For example, there may be an upper floor with small simple rooms, with or without baths. Always check the room out before accepting it, no matter how generous the discount. If the price doesn't drop far enough, don't hesitate to ask for a recommendation to a cheaper hotel. This is not only the ultimate bartering maneuver, it's also a good way to get directions. Mexicans are very casual in this regard and desk clerks will usually offer advice quite freely.
Longer stays make a good bartering point.
I'll give it a one or two-night trial, however, before suggesting to the manager that a discount on a longer stay would be very tempting.