Santorini at night is a whole other experience..I recommend taking a siesta so that you can reserve your energy for walking around the port town for shopping and dining. 
We like staying in Imeroviglio for our villa location. It used to be a pirate look out point.
If you can walk down to Fira or Thira as it’s sometimes called, it is a good way to get exercise and avoid looking for a parking spot. The view in Imerovigli or Oia is worth it. It’s also a nice break from the city center. Driving up to Oia could take 20 minutes and that’s best enjoyed at sunset.
Make an evening out of Oia…take your sunset family pics, eat dinner up there and stroll through the boutiques. 
I have been 4 times to Santorini and I know I’ll be back!! There are so many excursions to do so stretching it out over several days gives you more energy to enjoy each outing.
Follow this lesson plan to build trip itineraries with your family: