Pizza and bagels are musts in NYC. It'll be HOT and MUGGY in NYC, so dress ready for that.
I loved grabbing a bagel and the New York Times, a towel and heading to Central Park to people watch and lounge around. Ellis Island is a must do (same ferry as the Statue)
In LA, I personally think Venice Beach is a bit trashy but I guess for a tourist it is something to see. You don't need a lot of time, an hour is plenty IMHO.
Other things I like in LA are the Getty Center or Getty Villa (you could do the Villa and Venice Beach on the same day as they are just down PCH from each other). But you do need an appointment for the Villa (not the Getty Center though). Out by Pasadena is the Huntington Library and Gardens. Great botanical gardens that you can spend HOURS in. I also like hiking in Griffith Park - just be aware that if you go at dusk, while you can get great views of sunsets, there are also mountain lions.
I think the best thing about LA is being able to be outside year-round. The weather will be overcast at times due to "June Gloom" but it usually burns off and it worst at the beaches