Sardinia is full of hidden hiking trails, in mountains, along the coasts, covered by forests or just under the sun and surronded by la "Macchia", this local meditteranean vegetation that consists of small trees and bushes. You will get across all levels of difficulties, whether you are an experienced hiker, or you just do it for fun with your kids. Here below, a proposal of 7 paths, all located in the same part of the island (Ogliastra), ranked from the most accessible one to the toughest. In any case, remember that the best season for nature discovery is in May and June; if you do it in summer time, bring along with you a substantial set of bottles of water.
Close to the village of Lanusei, accessible from the SS198 that leads to Gairo, you will feel priviledged in this small wood area that offers opportunities to relax. There is a GREAT belvedere (view point) on the Mediterranean sea, and a play area for your kids. The Tomba dei Giganti is a historic site of interest and only takes one hour to visit.
Seui is a small charming village, at the west end of Ogliastra. To get there, wherever you come from, you will need to take sinous montain roads, so be careful with the car and do not exceed 50 km/h. Once you arrive in Seui, you have the possibility to do some hiking. The best is to park in the village, then ask a local about the Chiesa San Sebastiana (40 minutes walk from Seui). From the Chiesa, you can engage into a nice walk that leads you up the highest summit around, which is definintely worthwile (much wind up there :-)).
Another option is to head towards the Montarbu forest: ask a local how to get to the Caserma. Vegetation is more green, you have possibilities to visit a Nuraghe (historic tower in Sardinia), to enjoy some view points, or just to do hiking.
From the nice port town of Santa Maria Navarrese, you can reach Pedra Longa. It is a great path, offering great views if you look down the sea. Be cautious with kids, as you happen to be very close to steep cliffs at times. Total duration of the walk is 1h30, and is pretty much accessible to anybody. Just foresee to wear a cap, as the path is not covered by vegetation and you are just under the sun.
Keep in mind that in this area, a tour in quad is also en experience that is worth a try!
You can access Cala Luna by walk. Two options for you to do it: EITHER the well known 4 kilometers path from Cala Fuili (a beach located just next to Cala Gonone) OR through an alternative way, whose starting point is - I must admit - quite tricky to find. When you are in Dorgali, ask a local about where to leave the road SS125, and where to park your car, so that you get to the right place. The walk takes 2 hours and half, and you are supposed to follow a dry river path. Sometimes along the way, it is not easy to spot the right way forward. Be cautious, and take extra water :).
On kilometer 183 along the Super Strada (SS) 125, you will need to take right with your car and follow the signs. Multiple options exist to get down the canyon: jeeps can lead you up to a certain point, then you will need to contine walking. The descent is quite easy, but beware that the other way can be a struggle.
Cala Goloritze is one of the most beautful creeks worldwide (or let's say, that you will ever see). You can access it either by boat (still you have to stay away by some distance), or walking (3,2 kilometers length, vertical drop of 600 meters). The starting point is the bar "Su Porteddu", located on the Altiplano del Golgo, above the village of Baunei. Coming from Tortoli or Santa Maria Navarrese, you need to enter the village of Baunei, keep driving on the main road SS125, then you will see a sign showing the Altiplano del Golgo. Follow the road, and then you will need to continue for a 15 minutes car drive before getting to the parking. Note that in the peak season, 6 EUR are requested at entrance per adult (kids are not charged), quite a fair price as it is about preserving the creek and keeping it so clean :). If you are an average walker, it will take you 1h20 approximatey to reach the Cala, and 1h45 to come back.
To be honest, I never did this one. But I heard that it is possible to reach Cala Mariolu taking a secret hidden path through the forest. Still, at the very end, you anyway will need holding ropes to touch the white sand of the Cala (well deserved present). Good luck if you want to try. Recently (summer 2017), two belgian tourists got lost over there and had to call 112 to get rescued.