11. Festivals, days, and times sacred to this deity.
It seems as if Hestia did not have any special yearly festival that was particular to her, although as has been previously noted, she probably received the first offering from a sacrifice done during any festival.
Hestia did receive some special attention during the Noumenia, a festival celebrated on the first day of the visible new moon, which was the first day of the month in ancient Greece. Hestia was honored on this day along with Apollon Noumenious, Selene, and the other gods of the household (which could vary from house to house, or from city to city, although in Athens this often included Zeus, Hermes, and Hekate).
The Noumenia celebrated the beginning of a new month, and offerings were made in hopes that the household would be blessed for the month. Traditional offerings included honey cakes, barley cakes, fruit, wine, and garlands of fresh flowers.
In Athens no other festivals were allowed to take place on the Noumenia, because it was considered such a sacred day. It was meant to be a time to celebrate, feast with family, relax, and enjoy a fresh beginning.
Now I'm not a Hellenic reconstructionist, but in my personal practice I do honor Hestia on the new moon in a way that is inspired by the Noumenia - but that's a topic deserving of it's own post, at some point.
Additionally, I've come to associate Hestia with both Imbolc and Lammas. Imbolc is celebrated during the dead of winter here. Most years there's still tons of snow on the ground, snow and ice storms are common, the wind is breaking branches off trees, and although you can see the days begin to get longer, spring won't truly be felt for at least another two months. It also tends to be a quiet and reflective time of year. All of that makes it a perfect time to honor the warmth and blessings of Hestia.
For many Lammas is a time of grain harvest, bread baking, and first fruits, all of which are associated with Hestia in some way, particularly bread baking. It's an interesting time to explore that aspect of her.