What to do in Tulum?
 

Heading to Tulum with my daughters-Looking for yoga, mud baths, etc...
Good food
Safety
FUN!!!
Tips

Where in Tulum - beach front small hotel, all inclusive, or hotel in the pueblo? Are you renting a car? There's plenty to see and do in the area, especially if you have your own vehicle.
If you are not in an AI, downtown Tulum has dozens of small restaurants of every description. One of our favorites is La Malquerida, but we've had many good meals in Tulum. The small beachfront spas and hotels are 'yoga central' for this part of Mexico.
Of course you will see the ruins at Tulum, but the much bigger ruins at Coba is only a 45 minute drive into the jungle from Tulum. You can also do a tour of Sian Ka'an the vast wildlife preserve, snorkel at one of the many cenotes, take a snorkel tour, etc, etc. The whole area is quite safe. Have you been to locogringo.com? There is a wealth of info at their website.

Where are you staying or have you booked yet? I would try and stay along the beach road, and as far as I know there are no AIs in Tulum proper other than Kore Wellness which has a crummy beach. There are a couple of AIs with Tulum in their name but they are not actually in Tulum. Food is cheaper in the pueblo but it is hot during the day, so maybe lunch along the beach and dinner in town.
As far as yoga, tons of places have it, not sure about mud baths.
As zootsi says Coba ruins (you can still climb) is about a 40 minute drive from Tulum and you can rent bicycles or hire a tricycle taxi (site is very spread out). You might also look into visiting the nearby Punta Laguna Monkey Reserve.
Have not yet taken a tour of the Biosphere, although we drove once to Punta Allen and another time I drove myself as far as Rancho Sol Caribe for lunch. Check road conditions before leaving, it can be pretty bad after rains.

Lot's of options! Have you consulted a guide book? You'll learn all sorts of things you never even knew to ask!

A trip into the Sian Ka'an biosphere is fun. You speedboat across lakes and along twisty canals, see Maya structures, birds, manatees, the beach, and float a Maya built canal, lots of fun. The "sunset" trip was particularly nice, ending in a return across the lake at a spectacular sunset, to a wine and cheese social hour back in Muyil.
http://siankaantours.org/our-tours

In addition to the good suggestions above, there are often local festivals in Tulum with bachata dancing to a live band, costumed local groups, bulls, and lots of stands with food and clothing. Lots of local families, few tourists, safe.

Tulum is so much more than some upscaled hippie palapas and expensive restaurants along a small section of the beach road.