My family and I went earlier this summer and I too wanted to spend more time in other areas so did not spend much time at all in the Golden Circle (and totally skipped Reykjavik) and I don't regret it.
However, we did spend our first night in the Golden Circle, seeing several sights, and then saw Thingvellir National Park on our way out the next day. I think seeing Thingvellir and Gullfoss are a bare minimum, and must sees. Staying overnight in the Golden Circle gave us time to soaked in Laugarvatn Fontana which we really enjoyed.
I think the Myvatn/Husavik area is comparable to sights in the Golden Circle, especially with regard to the geysers and hot spots. We had intended to see Dettifoss, but were flooded out (roads and trails closed), so I was thankful we had seen Gullfoss in the Golden Circle.
The problem with the Ring Road is there's not a lot of diversity of landscapes; it's what you stop for that make it worth the trip And if you're trying to get to the North, it seems like you should start in there! To do this, I'd recommend you stay a night or two in the Golden Circle to see Gullfoss and Thingvellir (also Settlement Center if you can...highly recommend), then take a domestic flight from Reykjavik to Akureyri. You can pick up a rental car there and return it at Keflavík. Cut your ring road in half so you can spend time out of the car!
Not sure how much time you have, but we had 11 nights and we stayed 5 nights in the North (Hvammstangi 1 night, Siglufjörður 1 night, Myvatn 1 night, Husavik 2 nights) and side tripped (1 night) to Westman Islands. I was very happy with the time in the North, but doing so as part of the full ring road made it rough (as I had been warned!)