Our trip was in September/early October 2019, and we wrapped it up in Hania. One of the most enjoyable and authentic moments, which also involved food, was the Thursday market just west of the old port. In particular, one cheese vendor (with perhaps the biggest, bushiest mustache ever grown) had a fabulous cheese, but it was intended to be sold in whole wheels, not chunks or slices. We were leaving the next day, and an entire wheel was going to be just too much cheese. After a lot of negotiating, we were able to get a portion of a wheel, and hopefully he wears able to sell the remainder without too much trouble. There are markets 4 days of the week, at different locations: https://www.west-crete.com/chania-street-markets.htm
Arriving in Hania with our car, just before turning it in, was frustrating. The one-way street system made for very difficult navigating, and depending where you’re staying, getting a rental car out of town (and back in) for daytrips might be an ordeal.
We stayed right on the water’s edge of the port. Just a block or two to the south offered lots of fine restaurants. For nature (and a fair amount of walking, including a very long, downward stairway), the Samaria Gorge offers quite an experience, including close-up sightings of Kri Kri wild goats, unique to Crete. My husband used a private driver to/from the gorge, as we’d turned in the rental car at that point, but people take buses, too. You could use a rental car, and I understand that some people park at the top, walk down the stairway that goes partway into the gorge, then turn around and climb back to the start. That gives an appetizer taste of the experience, but going the length of the gorge is the real deal, with different sights and environments along the way. But that requires getting back to your car, if you parked at the top, and I’m not sure what kind of shuttle arrangement would need to be organized.
Festos is an amazing archaeological sight, more “authentic,” not painted up in an imagined, artificial motif like part of the Knossos ruins south of Iraklio. That’d be a fairly long drive, but if you want more Minoan sites, it’s outstanding.
The archaeological museum in Iraklio is also fantastic, but it may be mobbed with cruise ship tour groups like we experienced, and we moved to other rooms, then came back after the group left the first one, to avoid that. Best seafood in town is at Ippokampos restaurant - make a reservation.
Actually, some of the best moments of our trip were on the eastern side of Crete, and we didn’t venture west of Hania. Villages on the Lasithi Plateau, and Kato Zakros (including black sand beaches) on the far southeastern tip of Crete, were really special. That’s probably way too far from where you’re going to be based. The Lonely Planet guidebook can give you lots of additional suggestions.