Top recom for Crete

Where will you be to pick up the car? We need to understand where you will be before we suggest place to see and do.

Car pick up at Heraklion and staying near to old town of crete

Sorry we do not yet have sufficient information on where you plan to be. Old town Crete can be in Heraklion, Rethymnon or Chania.
so we know you will arrive in Heraklion. Are you staying there and you want some information about Heraklion?

I highly recommend that you stay in Chania, a beautiful town with a varied cultural history.
Must see- each town has an Old Town section which I recommend you visit.
December will mean that you won’t be able to do many of the warmer weather activities.
Crete has influences of its many conquests. Look for restaurants serving traditional Greek food and you will find Cretan influences. We ate fresh local fish grilled with a squeeze of lemon every single day of our month in Greece.

We are staying i1 night in Heraklion and 5 nights in old town of Chania. We rented our car from Heraklion.

Start by looking at the Lonely Planet Guide to Crete and/or the Rough Guide to Crete. Make a list of what seems appealing to you. I would start by looking at what is in Heraklion, Rethymnon, and Chania. See if the Saria gorge is appealing. In travel, I have a talent for locating and visiting under-appreciated sites and museums in addition to the most popular sites. Others may act like Chania is the only good city on Crete but that isn't necessarily the case. I only was in Heraklion and Chania. Chania has a maritime museum with 2 branches about 300 feet apart. One branch has a good display about the Battle of Crete in Worle War II. Chania only requires one to 1-1/2 days. Any additional nights in Chania are just for day trips. If you don't see any trips from Chania that look appealing, you only need 1 or 2 nights max in Chania. Heraklion has an archaeology museum that might have occupied me for over 4 hours, you can take a short bus to the ruins of Knossos from Heraklion, there are remains of old city walls, a Venetian fortress called Koules that has been marvelously restored; I paid to go inside and the rooftop level was open too. From here you get a good unobstructed view of the Mediterranean. Chania may have an archaeology museum with a collection of ancient coins in a vertical acrylic display case.

Ok thanks for the additional information. Chania old town is a delight. You can easily believe you are in the 14th century as you wander through the back alleys.
I have to admit though we have always visited in May or September. The good thing though is there is a permanent population so many of the tavernas will still be open for the locals. There are several good tavernas along the waterfront promenade.
Here are a few images of Chania.
Chania 2024 https://www.flickr.com/photos/stanbr54/albums/72177720318408008/

Chania 2022 https://www.flickr.com/photos/stanbr54/albums/72177720299646015

The archeological museum in Heraklion is spectacular. For us, it rated three diamonds in RS rankings -- make a special trip there.