You will have no trouble finding a room. Be resourceful, look for hotels in the medium to large to very large towns . Any place where a federal highway passes a town of , say 7000 population is likely to have at least one place for lodging. . Bigger towns , and those near tourist draws are probable targets , look around the central plaza, look in the side streets and alleys .ASK the locals where the hotels are.
Seaside towns and resorts are likely to have good supplies of hotels but these charge higher rates and also draw the big crowds on holiday weekends which actually may nearly fill hotels available. This is particularly so in the Mayan Riviera where the snow birds migrate .
WARNING : do not go to CELESTUN during a holiday weekend. It is a pretty enough little seaside town but on certain holidays they have a festival and set up 300 loudspeakers of 1 million watts each and blast LOUD music/noise all over the town all night until 6 am. Okay, maybe I exaggerate a bit on their power , but you will not get a wink of sleep . Been there done that. It is very nice on a quiet midweek night.
HOLBOX on Isla Holbox is interesting but can fill up on holidays.
In Cancun you can always find reasonable (low! )priced rooms at the hotels along the north edge of downtown along Mex 180/Av Lopez Portillo.
Finding a hotel room in the 'normal towns" will be no problem, they do not draw massive crowds , just the locals having parades, parties, concerts at the plaza and going home.

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