I can only think of one country where my first visit was with an official delegation and subsequent visits as a private citizen, and that was Qatar. Needless to say, the Qataris know all about hospitality. I kinda missed having a fleet of white Lexus limos hanging around the hotel in case I wanted to go anywhere, but hey, that's the breaks.....
There are some other countries like Angola where I would never even consider going back except with an official delegation. One of the most miserable weeks of my life.
Edit : Cote D'Ivoire was another country that I visited first with a delegation and then stayed on an extra day on my own. Contrary to popular perception, Abidjan was easy and safe enough to explore on my own and I actually enjoyed hitting the street and finding some excellent restaurants a lot more than the official meals and hotel buffets.