Hi! Great question, and one without a single right answer, as you probably assumed!
Here are the areas that come to mind for me, starting from most crowded and touristy to least:
– Reykjavik
– Golden Circle
– South Coast
– Snæfellsnes peninsula
– Westfjords
Any two would make for a great vacation, so I don’t think you can go wrong. The Golden Circle is wonderful, and offers lots of things to do. It will be crowded in September, though not as bad as the summer months.
Snæfellsnes offers my favorite hike for kids in Iceland; see the second picture in this post about Snæfellsnes (written by my son!) It’s not a super long hike, probably under an hour each way even if you go slowly. I’m not sure if you were looking for longer day hikes? There are lots of other hiking options in the national park on Snæfellsnes— you can ask in the visitor’s center what might be a good option for you.
So to try to answer your question, I’d say Snæfellsnes can be one. Then you could add the Westfjords if you really wanted to get off the beaten path, though it would be close to a 6 hour drive from Hellnar to Ísafjörður. Any of the first 3 places above would be a great addition as well: Reykjavik if you wanted a city, the Golden Circle to see the classics, or the South Coast to see more of Iceland’s natural beauty.
Hope that helps?