I think Ziggy's is probably your best bet for a start, comfy beds, good food, nice beach. As mentioned, it's more crowded than other places in Tulum, but it still won't be anything like your AI beach.
From there, you can walk south--are you walkers? You can walk all the way down to Rosa del Viento in about a half an hour, maybe 40 minutes, you can stop at Om and other places along the way to see what else there is for future trips.
Another option is to go down to Las Ranitas--they let you use their pool if you eat and drink, not sure if they charge for the beach beds for non-guests, but it's a nice stretch of beach and not usually crowded unless they're having a party or something.
La Zebra is not a beach club, and while if the hotel isn't full they may let you sit on a beach chair, their policy is that they are reserved for hotel guests only. They have nice decks and lounging couches if you'd like to stop for a drink--their mojitos are justifiably famous (made with real, fresh-pressed cane juice, you can show the kids how they do it inside at the bar).