Cross Country

I'm planning a trip driving from Los Angeles to New York City, I live in
the UK. I've checked out flights and car hire but I could do with some
advice.

How long would a fairly relaxed journey with time enough to detour
slightly take? I was planning on three weeks. Has anyone done a similar
journey?

I don't know what I should check out in particular. I would like to see
some sights that are a little different that the usual tourist traps.
Any advice?

Any survival tips would be cool, like how easy is it to navigate US
cities in a car, how expensive is a gallon of gas, should I book hotels
in advance or just turn up at motels, basically anything like that.

It seems daunting to plan this stuff right now but I'm determined not to
wimp out and go to Spain!

Regards

Geoff Pedder