I started typing this the got distracted. Basically agree with everything
@deepsea21 said. Casa Mexicana or one of the B&Bs might be good for you if you want breakfast and want to stay in town. Someone posted on Hotel Plaza while I was typing this.
Food budget is really hard to say. If you are eating tacos it would probably as little as 100 pesos (5 USD) per person per day , if you are eating at nice restaurants and ordering wine you could average 700 pesos per person per day if not more if you drink a fair amount.
To give you an example of price —Cozumel Dreaming is around 430 pesos per person all you can eat. Probably figure 500 pesos per person including tip. I can’t remember if it includes a drink or not. I have primarily been ordering delivery due to Covid. (Eating at the restaurant is the way to go during normal times , but small indoor spaces not exactly high on my list right now ).
The flip side of this that is Mister Taco(decent walk from the waterfront , but the taco place I am most familiar with ) I think the tacos are in the 20-25 pesos range and average person probably gets 3 tacos (light eaters might get 2 and heavy eaters might get 4 or 5). Total average bill with drink probably less than 100 pesos
Given you are talking about 2 people for a week , I would probably just get 6,000-7,000 pesos my first day and see how long it lasts. I would just recommend a grocery store, but using one in a bank branch clearly works also. In addition to food, you also have dive tips and booze you can spend it on. The crews don’t really care whether you tip in pesos or dollars but it is easier for everyone if you just tip along the way rather than trying to do something on credit card at the end. At most shops your DM and captain will likely change during the trip so sorting out who gets what at the end can be a pain. Point is that if you aren’t spending as many pesos as expected for food/booze (a rare occurrence ), you can shift to using for tips. For two people diving a lot the tips can make a dent in your pesos fairly quickly, especially if you are doing 4 dives per day as I think you said was a possibility
I would lean against a car for the trip based on what you are saying. If you are staying downtown and diving with a shop that uses one of those piers it is clearly not necessary and more trouble than it is worth to rent a car for your entire stay. I actually haven’t dove from a downtown pier in 15+ years so don’t know who still uses those piers. Even you are leaving from marina, taxis are still very plentiful and pretty cheap (just ask the cost before you get in the taxi ). They are plentiful during normal times and now without the cruise ships the supply is 3X the demand. Only question would be your Covid risk aversion. You had said you were in medical field so assuming you have been or soon will be vaccinated so risk of your getting seriously ill here is low. However even if you have been vaccinated if you get a variant where vaccines are less effective you will test positive and get stuck here for a while (though most of the data says you will not be very sick in this case ).
I would consider renting a car for one day and going to the east side at some point during the trip, though this is something I would play by ear.
Just as further background—Parking is a lot more of pain than it once was, though there are lots but the hours can vary. Over the years, the municipal authorities have widened the sidewalks on some streets and put in bike lanes on others. I don’t mind the nicer sidewalks or the bike lanes, but took out a whole bunch of the parking on the island. I have my own car , but I generally hear good things about Rentadora ISIS. I actually used to rent from Hertz.