Can't advise on specific AI's in Puerto Plata, but consider Cabarete, 25 minutes to the east of Puerto Plata airport. Why Cabarete? Young crowd, casual, and fun nightlife. Also lots of opportunities to kite sail, windsurf, surf, bike, etc. or take lessons for any of these. Note, September 1 starts slow season, so things will quite possibly be a little slow whatever resort/town you decide to visit.
Several options if Cabarete sounds like fun to you:
1) Go with an AI in Cabarete if that's what you want. Unlike one of the POP resorts, you can easily get to the center of town from several of them here and aren't "trapped" inside the AI for your whole stay. Take a look at Viva Wyndham Tangerine (a little out of center of town) or Azurro (in center of town).
2) Book 2 bedroom/2 bath condos at Ocean Dream or Cabarete Palm Beach Condos. Both of these are on the beach in walking distance to everything. CPBC more centrally located, OD is newer & more luxurious. All of these will sleep 4 people comfortably & checking
Hotel Cabarete Palm Beach Condos and Studios the rooms will run you $110 a night for true ocean front in September (7th night free). Ocean Dream will be about the same price for ocean front, but not ocean view.
Ocean Dream - Luxury condos for rent in the center of Cabarete, Dominican Republic You'll even see some 3 bedroom/3 bath condos at Ocean Dream if you have a large group. Verrrrry nice accomodations.
3) Cheaper options exist for individual hotels such as
Cita del Sol,
hotel Kaoba, and others if you want individual rooms. Again, these are in center of town & easy walking distance to several dozen restaurants.
Good luck