I have travelled alone, but never had a road by myself.
Solo travellers head off to backpacking routes (for yourself, head south to latin america or Brazil).
If you have the money do Europe or Asia.
For a road trip, the costs will be lower the the experience better with some friends. Even one friend is enough.
Or forget friends, start a blog, and try and find people to travel with. Nothing like a couple of Danish backpackers to make life interesting on a trip.
Where to go...well you should tell use where you are starting and how long you have.
But in the US the best trips are north to south (or south to north) because the US is bordered by the previously british controlled canada and the previously spanish controlled Mexico and these are 2 major influences on US culture, resulting in a journey across the land but also culture.
You can also do coast to coast as well.