For the group going to Chalki they might just take the local bus. Return fare will be less than a car rental. The car allows then to do a bit of sight seeing on the way and back.
We have done part of the trail to Moni but stopped when it started to go uphill. I subsequently read a report that someone stronger than us did the whole trek only to discover that there is really no way to get back to Chalki from Moni other than to walk back. Need to think of these things.
There is a circular hike around Chalki. It is 4 to 5 kilometers and takes about 3 to 4 hours however for the most part it is easy level walking.. This hike is described in the book walking on Naxos by Dieter Graf. Two Churches in the Olive grove. From the bus stop on the main road walk back 150 meters and look for the path down to the left. It takes you to the village spring and wash house then the Byzantine area. Turn around and go back to the spring to begin the hike, The book does give accurate information but is pretty minimalist on the distance between each segment. For example ".you come to a concrete track. go left straightaway passing a large oak tree and left at the fork." That sounds simple but we didn't realize how far that was. It turns out, about 15 minutes later there was an oak tree. Its a good idea to get that book at Zoom book store on the waterfront promenade
The hike is on this album. Its the last 23 images on page on e and the first 11 on page two.
Ten Days in Naxos 2015 https://www.flickr.com/photos/stanbr54/albums/72157656336387898
This hike takes you past Byzantine era ruined buildings, rock walls lining farmers fields and olive orchards, two tower houses and several Byzantine churches. I Bring water and perhaps a light snack. When they get back to Chalki they will want to rest at a taverna for an hour or so then explore the village another hour and probably another beer before returning to Naxos town. That will take care of your first group.
Your second group might want to continue on from Chalki with a stop in Filoti. You are really getting into the high mountains now and you will be experiencing some swithchbacks but for the most part are just one at a time not a series of switchbacks. There are little pull outs at the top of each scenic spot so the driver can actually see something other than the road. I know driving in the mountains is a concern but there is virtually no traffic and speeds are very low. The traffic you do experience might be large truck or buses. I just pull way over to the right and stop to let them go by.
Naxos Mountains and Villages http://www.flickr.com/photos/stanbr54/sets/72157632110674306/
Its worth stopping in Filoti and taking a wander around. Its built on the side of a mountain and getting into the residential area just beyond the main road is a step into the past. A little rest in one of the tavernas under the trees in the main square is always a great experience.
Now continue the drive to Aparanthos. This village is much older and has Byzantine and Venetian buildings. The streets are paved with marble. There are interesting shops and tavernas with valley views. A great place to stop for refreshments and a rest.
Images https://www.flickr.com/photos/stanbr54/38394630051/in/album-72157689937827955/
This hyperlink is from last September visit to Aparanthos. It is one picture. When it opens use the arrow button at the right hand side of the picture. There are 23 images to the end of page one go to page two and there are 11 more.
Now turn around and return to Chalki where you can visit the village. It is charming relaxed and has the Kitron distillery that has complimentary tastings.
There is no reason to go further. These tree stops are more than enough for one day. Greece is not about how much ground you cover its how you take the time to truly experience what is there. Notice I included a taverna stop in every village. Just relax take it all in.
