I will be staying in playa del carmen for 4 nights in january and would like to know where the best places to go are. I am interested in anything cultural or hstorical but also like an adventrure. Thanks in advance

Maya ruins at Tulum and Coba. Coba has a pyramid to climb, and bikes to ride (or pedicabs). Alligators across the street in the lake and a monkey park nearby. Tulum has a beautiful, but often crowded, beach below the ruins.
Boat trip into the Sian Ka'an biosphere from Tulum with a Maya run tour company.
Swim in a cenote or three.
Snorkel with huge turtles and rays in Akumal.
The shopping area where the locals shop in PdC for cowboy boots and gear, and stylish non-US style clothing.

With only 3 days I would only do one excursion. Catch a colextivo to tulum and see the ruins and then go to the Puebla for lunch and if want to very busy, go to coba from there. It's more shaded so I suggest tulum first. One day just explore PDC and relax on the other day. You don't have time for much else

I'd go visit one of the ruins, probably Coba since it is in the jungle so has some shade and you can climb the pyramid there, Tulum is pretty crowded and gets overrun with tour groups unless you get there when it opens at 8am. Admission to both is a bit less than 70 pesos pp.
I am not a fan of the beach below the ruins at Tulum instead take a taxi (if you don't have a rental car) and head to one of the beach clubs like Ziggy Beach Club at Cabanas Tulum or La Zebra. The food in the pueblo may be better and cheaper but it is too darn hot for me during the middle of the day. Much better at night.

If you don't already have a copy, I thought the Moon Guide particularly useful.

Eat at El Fogon!

SImming at Akumal with turtles was a highlight of my trip in Mexico.
Avoid xcaret
Tulum is disappointing is you have visited other ruins. Do chichen itza (so ?) instead

With only 4 nights, a loooooong, grueling tour to Chichen Itza (or even better, Ek Balam) from PdC is something to consider very carefully before embarking.

I agree that Tulum's ruins are not the most spectacular specimens of the pre-Colombian era. But the setting is impressive nonetheless, and so easily reached from PDC. No good reason not to go, with only 4 days.

With only four days.. I would do Tulum ( its easy to get to, and I love the setting) and hit beach after for lunch and swim. If you do go to Tulum wear a hat and take water..its hot there and little shade and no available facilities inside the park.

I would also suggest if you want a thrill day out,, Xplor , easy to get to also.. take collectivo.
Ziplines, cave swims and paddles.. off road vehicles( but you are on a trail). Good included lunch but no booze as the ziplines dont want drunks..

If into water more.. then try Xel Ha.. also all inclusive( drinks and lunch )

Difficult to add to the answers above... they all sound reasonable !