We call Cancun "the concrete jungle". Glad I saw it, no desire to stay there again.
Playa Del Carmen is nice, though different than Cozumel. I like its quaint atmosphere though I prefer Cozumel since it's easy -- and a lot of fun -- to explore the island on your own. We've always felt safe on Cozumel.
Cozumel DOES have beaches to offer, but as mentioned previously, you'll have to stay south of town, which means taxi rides can get pricey. Solution - rent a vehicle.
I'd stay clear of the resorts situated close to town and close to where the cruise ships dock unless the taste of diesel fuel and the view of one or more large cruise ships parked out front appeals to you. We stayed at the El Cid and hated it for those reasons, and the fact that they provide use of their facilities to the docking cruise ship passengers. The only reason we stayed here was because it was a complimentary stay as per a time share presentation.
Regardless of the distance of lodging from town, I'd recommend renting a vehicle for your stay, as the east side of the island is a must see for a day trip - lots of beaches and restaurants to stop at, great views, and shops along the way. We stop at Chedraui before heading to the east side - stock a cooler with ice, refreshments and snacks and make a day of it. San Francisco beach has shower facilities, gift shop and restaurant on site, and a raft you can swim out to and I believe they have wave runner rentals.
I've stayed at the Allegro in the past -- years ago -- I think they're under new ownership now. The Occidental is nearby. But, we loved the resort, the beach and the location.
On the flip side, we've also stayed at the Coral Princess (didn't go A/I) just north of town - a smallish resort, quiet, no nightlife, but what we liked about it was that you could just drop in the water next to the reef from the ladder and snorkel there and never had to worry about boat traffic. Plenty of fish to see. They have a small man made beach, and rooms are either jungle or ocean view. Ocean views are spectacular. This is much closer to town.
Cozumel is not known for its night life, but San Miguel can be pretty busy during the day and plenty of great restaurants (please do try local food even though you are going all inclusive - there are many decently priced restaurants with excellent food that you'd otherwise miss staying at an A/I).
Good luck in your decision making.