It's quite doable.
Do a thorough walk-around and use your camera / smartphone camera to take photos from every angle, and be sure everything is documented on the rental firm's paper (in Mexico, or in the US, or wherever!) Be sure to check spare tire and tools - if anything is missing it will be charged to you, not to mention the inconvenience of a flat with no tools. Be sure to note any missing hubcaps or rear view mirrors, etc. as they will also be charged to you if missing and not documented previously.
Get the full coverage insurance - the insurance company is your bailor / guarantor, and be aware in many policies glass breakage, partial theft (items like rear view mirrors) etc. are not covered.
Do watch the "topes" (or "tumulos",
lomos de burro,
lomos de toro, etc. in different countries) as mentioned

,
which may not be marked, as well as unmarked and sometimes large potholes, and do be prepared for an occasional stop to check papers, sometimes baggage, etc. by very armed uniformed officials.
Be aware some animals may be using the road, and a breakdown around the cure may be indicated by some rocks or branches on the road - which will not be removed when the vehicle is fixed and moves off.
Do NOT drive after dusk, do not drive in the dark and do not drive at night. Do you sense a trend here? (I've driven in Mexico under all kinds of conditions since the late 1950s, and I will try to not drive at night - that's when the animals will come out, as well as drunks, and sometimes more nefarious people.)
More Diesel pumps in Mexico stations, often the same type filler as gasoline / petrol; be aware (if you need Diesel, be sure they filter it - the filter will be prominent and it will say
"filtrado"). Also be aware one tips the guy in the petrol station who pumps for you and maybe cleans the windshield; a five peso bill is more than sufficient (about 40 cents US), and be sure the pump is "zeroed" when they begin pumping and they stop when you want them to. Also be aware they are quite willing to check your oil and - short dip it so you buy a liter, but you need to double check or you may find yourself with too much oil in the crankcase. There is one type of petrol - Pemex, the national oil company. I try not letting the tank ever get below half-full, because the next station may be distant and the replenishment for the week may not have happened.
Originally Posted by
mmdough
Thank you all for your suggestions. Just to clarify, we do not plan to stay in Cancun much but will travel to Valladolid, Merida and maybe Tolum where hopefully will be much less 'touristy'. I do like the idea of less stress and not having to deal with car rentals but also concern that it will not be very convenient if we need to rely on public transportation to go places.