Re: To drive accross the US
I have drove in the USA a number of times but admittedly not across the whole country. Zag is correct; you would see very little on the interstates and if you plan to do it in 10 days. The country is much larger than people realise sometimes. I drove for hundreds of miles and then looked at a map and realised only a tiny fraction was covered.
That said, the interstates are fantastic for getting from place to place quickly. However don't take on too much because you spend too much time driving, you end up with a sore back and some very cranky passengers.
Bottom line; my advice is fly to New York, hire a car if you want and spend say a week travelling around the north-east i.e. New York, Philadelphia and Washington (really worth it, I did it last year) and then flying onto San Diego staying with your relatives and hiring a car if you wanted to and travel around the area e.g. LA, Tijuana (Mexico), perhaps even a couple of days in Las Vegas. I don't know how much time you have.
That way you would enjoy the trip much more and get a lot more out of it rather than spending endless days on the road.
One other thing of note, one way car rentals cost a fortune particularly in the case of the distance you are talking about. Flying from New York to San Diego would be much cheaper.