This will be challenging. By some measures, Playa del Carmen is the fastest growing city in North America (I say this from Seattle, the other now-overcrowded Fastest Growing City in North America - both suffer from cruise ships and decades of promotion and resultant unchecked growth).
I've visited PdC many times over the past 30+ years. Today it's a far cry from the quaint little fishing village with a single telephone that I first found. It's still a useful hub for jumping off to better places further afield, but I wouldn't spend any more time there than I had to.
With just 2 days, I don't think you will be able to find what you seek: authentic, natural and/or adventure experiences without crowds of foreign tourists. Those can still be found in the region, but it'll take you the better part of a day to get to them (and as much time to get back) so...lo siento.
I'm guessing from the way you wrote your post that you have not been to this area before.
You need not worry about heights. With the exception of high-rise hotels, and some of the great (but crowded) ruin sites (most of which you are no longer allowed to climb), theentire region is as flat as a pancake, with no elevation gain at all.
We are both hikers and don't mind killing ourselves as long as the view at the end is worth it.
Within a day of PdC, there are no hikes involving elevation gain, and all views are going to be of the waterfront - most of which has no shortage of development. Yes, you can find places on the coast that are less developed (and even undeveloped) but they require some travel.
I think you need to come to terms with a basic conflict in your expectations: You don't have enough time to really get away from the crowds. So wherever you go, you'll be among plenty of tourists, and probably large tour groups, and a lot of pretty crass mass tourism. Make your peace with that - or else add a week to your trip, and put a day's driving between the tourist coast and your destinations - there are plenty of them, but everyone (and I do mean everyone) goes to places along the coastal strip near PdC, so you need to get away from there.
30 years ago, unspoiled places were easy to find there. Today, it's one of the most intensely cultivated tourist areas in the world, and it feels like it. It is what is is. Still great if you put in the time and effort to get away from the tourism machine, but if you can not or choose not to, then be ready for what it is.
Good luck.