Those are all good; and that's a fairly large number of things you're out to see. I'd also suggest doing something outdoors while you're in Nevada/Arizona - there's lots of native ruins and generally beautiful terrain contained both on reservations (some of which you probably *can't* access) and in national parks (which you probably *can* access) that you could observe/visit, as well as the Grand Canyon in general. Some of the most epic ones will probably require an additional amount of driving into the four corners region (that's another day or two). If you go ahead with any of these activities, hydrate appropriately (and remember you're also going to be talking about a substantial altitude gain over Denmark in the southwest US).
In addition to Hearst Castle, you might also like the Winchester Mansion in San Jose.
As far as theme/adventure parks go - Universal Studios is neat, Sea World is neat, you might as well pony up and see Disneyland as well though.
I'm not really familiar with Vegas proper - I know there's *lots* of entertainment venues in the major casinos, but I have no idea what's good and what's not good, which casino/hotels are ideal for staying in (I'm not implying any are bad, I'm sure there's a "ranking" though), and so on. Hopefully someone else chimes in there.
Oh, and the point about In-N-Out is both good by itself, and gets at a broader point: the food. Try it. I don't know if TexMex/Mexican food is very common in Europe, but some of the best restaurants around (outside of Mexico/Central America proper - which is a whole 'nother adventure) are located in the part of the world you're going to visit.
Within NYC itself - I have no clue really. Never been myself.
I know there's a lot of tourist
traps attractions like the Statue of Liberty/Ellis Island, various sporting venues, and so on. As far as electronics shops, since you mentioned them, J&R is supposed to be a sight to behold in NYC. In California, there's WeirdStuff and HSC (Sunnyvale and Rohnert Park (N of SF)) which have both been featured in various publications (one of them was featured in the NY Times, I forget which) and on Mythbusters. There's also Fry's Electronics which is a regional chain throughout California/Nevada/Arizona/Texas (http://en.wikipedia.org/wiki/Fry's_Electronics#Store_themes).
Depending on how much additional driving you want to get into (I may be wrong, but your California/Arizona/Nevada trip probably will cover more land than the entire nation of Denmark), you could go up into Utah and see the various religious (LDS) monuments there, as well as Moab (outdoors, 4x4 stuff, camping). That's another 6-8 hours beyond Vegas though.