NC would be great, but...
In my opinion, you must consider North Carolina. Whilst residing in the USA, I had on occasions to make journeys to Wilmington for the beach as well as Pisgah and Tsali for the trails.
I must say, these places are at opposite directions of the state but nonetheless may be convenient if you were to make a flight into Charlotte and each rent cars
pisgah and wilmington would both be great destinations...only they are at least 5-6 hours driving time apart, and that's hauling!
I second separate vacations, that's what we do once a year, my wife does the beach at NC, and i hit somewhere rideable...moab, fruita, so-cal, this year its az...everyone is happy too!