The isla has always been a day trip, not a destination--but with more and more Americans and Europeans seeing it as a destination, it's starting to accomodate. There are no hotels, and probably never will be thanks to ejido law, which is to complex to get into here. But there are getting to be more and more little rooms-out-back to rent, and camping is extremely doable.
The nicer places get grabbed up for the season, of course, but if you poke around you turn something up. Best bet is NOT to just show up on the island looking for a bed, like so many backpack types are doing. Best bet is get a cheap room in Mazatlan (where there are LOTS of cheap rooms) and come over for a day of swimming, beachfront sipping, and house-hunting. Ask a couple of people, not just one. Victor, at the eponymous restaurant, is a good source, because he knows everybody and is not renting anything himself.
The main places you hear about are Lety's and Marisela's. Overpriced, dingy shitholes where you use the bathroom of the restaurant, you want my opinion. But they generally let renters run a bar tab. You can sort of walk along the beach looking past the palapa places and see who has just added a sleeping room.
If you are down for the season and want something nice or big, check with Hilaria at the "Puesto del Sol" restaurant, in the middle of "Palapa Row". She has two new apartments--and a nice house that I lived in for a year. Or call her at 044-69-87-50-37, write to Hilaria Navarro, Domicilio Conocido, Isla de la Piedra, Mazatlan, Sinaloa, Mexico. It's a simple one-bedroom (though I've seen a dozne hippies live there) with a shaded porch where the ducks chase the chickens around, view straight out at beach, across from a pizza parlor, and I put in on-demand hot water in the shower. She charges more every change of tenants, but we're probably talking around $120 a month.
At the north end of the beach are a few possiblities. The "Casa Zen" is a great little commune-style place with wonderful buildings--but you never know if they are in the mood to rent or not. Walk in and ask, it's worth it to see the place. Next door, at what everybody' calls "Mama's", the northernmost palapa restaurant, there are three or four very spartan brick units for rent--no kitchens, you eat at Mama's. Whose son goes fishing every morning, so she always has it fresh. A pretty good bet for a week on the Island, actually. You're paying maybe $3-4 U.S. a night.
Another good possibility that nobody ever finds out about is to walk across the spit that separates the Isla from it's own offshore island, Goat Island--the spire of rock seaward. There are a few little places there, most of them geared up to serve flash-crowds of day-trippers who arrive by catamaran, blitz out, and go back to Mazatlan. Obnoxious folks, but fun to watch playing volleyball. Anyway, the last of these places says, "Pizza" and they do make pizza, and is it ever awful. But their other food is good, and the owners, Carlos and Victoria are just the salt of the earth. They will rent you a third-world lean-to off the restaurant, or one of their new cement rooms out back. Cheap. Like living with a family. And there's the nice little hook beach right out front, fishing off the rocks, easy walk to the Isla beach, easy access to boats to town.
Or, you can usually work out something to camp at a restaurant. Lety or Victor will probably let you pitch a tent if you eat there and maybe help them put the chairs up at night. If you want more solitude, walk up the beach a mile or so and tent out. Best bet is to build a palapa over your tent for shade--no problem because there's a lot of driftwood, and palm fronds are pretty easy to find, considering the beach is lined with about a zillion trees grown for commerical coconuts. Bit thing--sand fleas. Have repellant, don't wear outside clothes into your bed or bag, etc. Buy water and food from the market near the pier in the village. Just you and the breakers, and your occassional passing tractor.