Just got back from our honeymoon in the Caribbean yesterday ( we had a lovely mini moon straight after the wedding also!) We decided to have an unplugged honeymoon. 2 Weeks no internet, no TV, no news. The only exception was he could check the football scores. I can highly recommend it. We talked lots and it was great not being glued to our phones. We will be doing this again on our next holiday. It made it super relaxing.
Just wanted to recommend it to others. It's a great way to start married life just concentrating on each other.