We are going on group tour of Greece which ends with 4 days in Crete on May 23rd: "...visit Knossos Palace and the Heraklion Museum, join a Heraklion food tour, savor a welcome dinner in Chania, discover the traditional villages around Chania on a guided tour, and participate in a dance lesson."

We would like to spend 3 more days in Crete on our own. Any suggestions?

Phaistos. More time in Chania. Maybe Rethymno. Maybe hike through one of the gorges.

You might find some useful information in my trip report. The section on Crete begins with post # 48. With Gratitude for a Glorious Solo Month in Greece

Hi there! Good idea..Crete is huge and you need these extra days to get a feel of the island.

Some suggestions particularly if you are ending your trip towards Chania.
Rethymno old town
Arkadi Monastery, Ancient City of Eleftherna with a small modern museum, pottery village of Margarites.
For olive oil exprerience I would recommend Bioelaia Astrikas Estate, they give you a tour of their olive press and there is a nice restaurant on the top of the hill looking over the olive grove.
Botanical Garden, in Chania region.
Ancient city of Aptera Archaeological Site
To name some.. But it really depends on what you like.