You have 4 options getting from Akureyri to Reykjavík.
You can fly directly to the Keflavík Airport, or to the Reykjavík domestic airport depending on the time of the day. Time is 45 minutes.
There are busses for you to take. They make stops at gas station/restaurants every now and then. It will take about 6 hours, the same as with ...
For the flights, as I understand it as long as the overland leg is shorter than the flown legs and the flown legs are on compatible airlines it's normally possible for the two legs of such a trip to be booked on the same ticket with each leg being priced at "half return" pricing.
Google flights offers a "multi-city" option that can be used to look for such ...