We recently spent 4 nights in Cinque Terre, Italy.  We chose to stay in the town of Vernazza which allowed us to easily take the hike from Vernazza to Monterosso al Mare (1 of the 2 coastal trails currently open).  The plan was to wake up and go so that we could beat the August heat and the August tourist rush on the trails in the afternoon.  
At the start of the hike, shortly after the ticket checkpoint leaving Vernazza.
 We started our hike around 9:00 AM and finished 2.5 hours later at 11:30 in Monterosso al Mare.  We were welcomed with beautiful views and a sometimes steep and crumbly path along the way.  It was hard work as the ascent is a steady uphill into the mountains, it then levels out for a short while with bouts of up and down and then it descends even more steeply into Monterosso al Mare.
Mindi, my cousin, leading the way out of Vernazza followed by Eliana and Jonathan
The views from above are breathtaking.  The town looks as it does in catalogues and brochures. It is charming and brightly colored and looks as though it is painted just below you.  You can see in the photo that the beach is almost vacant at this time of day.  We would wake and look out our window at the locals who I am sure were enjoying the peace from the tourists.  It is definitely a nice time to start a hike or wander through the towns as you can see them without feeling like you are being herded in a certain direction (which is how we felt when we got off our train at 3:30 in the afternoon the day before).
Eliana very excited to find heart shaped leaves along our path

Viewpoint and nice place to pause after going uphill for quiet some time

Eliana, pretending to be our tour guide, announcing which way to go along our path
About halfway up you can see both towns at once: Vernazza, where we came from, and Monterosso al Mare, where we were going.  The entire journey is along the coast with views below of cliffs and rocks down to the Sea.  The Sea was a beautiful blue and seemed to urge us along as we had bathing suits packed in our backpacks.  The plan was to jump in the water after arriving in Monterosso.
Vernazza far below to my left

Monterosso al Mare far below on the other side

Views of the Sea from above with the cliffs down into the water.  Amazed and proud that we climbed up and over from Vernazza, which looked so small and far away
Happy (and relieved) to see where we were going - Monterosso al Mare. 
The children did wonderfully.  We hiked this path with a 2.5 year old (in a backpack), a 5.5 year old (who fluctuated between "friendly tour guide" and "whiny grumpy tour guide" based on if we were headed uphill or not) and an almost 13 year old.  The uphill portion at the start of the hike is difficult, however less difficult than if we had done the hike in reverse.  The downhill portion seemed to last forever and I really felt for those who were walking the route in the opposite direction as us.  I would highly recommend taking trail from Vernazza to Monterosso rather than in the opposite direction.
 The path is narrow at some points and there are drop-offs in areas that would not be safe for very young children.  I didn't feel comfortable letting Lucas (age 2.5) out of the backpack during the hike due to safety reasons.  Eliana (age 5.5) was able to complete the hike on her own with the help of a hand to hold during unsteady portions (loose rocks), or steep steps (the descent into Monterosso al Mare).
Bridge over a water running down the mountain.  

A happy (and sweaty) girl to be "almost" at the beach
The beaches at Monterosso are long and deep.  And, there are several to choose from.  We chose the beach closest to the trail exit, which served its purpose for us.  It was free and not too crowded.

 We had happy and tired children after the hike, but everyone was very proud of themselves!
Link to more photos from our trip to Cinque Terre
Link to our other hike in the Cinque Terre: Corniglia to Vernazza
Link to details on our stay in: Vernazza, Cinque Terre