My husband and I went cave diving last October, and we stayed at the Wyndham Maya, which is an all-inclusive. Because it was low season, we got a pretty incredible rate -- It was something around $120 a day for both of us. I don't know if that's what you consider budget or not, but when you realize it includes all your meals, it's a pretty good price. This WAS in Playa, which is not all that convenient to the cenotes, though. A rental car is a HUGE expense, but I believe some of the dive ops that do cenote tours will pick you up in Playa. The ferry to Coz from there is $24 round trip.
There are some small hotels down in the Akumal/Tulum area as well, but some of them look rather . . . questionable.