As you research the places and attractions you identify, place sticky notes on the map. Once you are

You've pretty much just listed the two terminal cities for I-80, so with nothing else to go on, it's hard to tell you any other route than just get on I-80 and drive 'til it ends. As for pitfalls, the two biggest would be not leaving enough time to make the trip - 5 days minimum just for the drive plus any time you want to spend seeing things along the way - and not having any ideas for what you want to do other than get there.
We have approx 2-3 weeks so it looks like time will be on our side. This is our SF/NY segment of our trip. We are leaving Sydney, Australia on 15th April by cruise ship and docking in SF 29 days later. We will then hire a car and make our way to NY. Following that we want to go to Mexico. If we go by road, what route would you advise or should we fly because of the hire car problems we may encounter. After Mexico we will try and get a cruise culture in the united kingdom ship back to Australia.
For routes, as Buck mentioned, I-80 is the direct route, but the bigger question is what do you hope to see and accomplish during your trip. Once you've got some ideas, other than 2 points on opposite ends of the continent, then it really becomes a matter of finding the roads that fit.
As far as what to do in the middle, culture in the united kingdom we have not idea what you are interested culture in the united kingdom in, so there's no way for us to narrow down the millions of possibilities. At the very least, I'd suggest getting a big map and simply looking to see all the things that are in the middle. Once you've got at least a basic outline of an idea, then we can start helping you put a plan together.
If you were thinking of taking a rental car down into Mexico, that WOULD be a problem. Most rental car companies in the US do not allow their cars south of the border ... for very good reason. It would be almost impossible to do a one-way car rental from anywhere in the US and dropping it off in Mexico, for that reason.
As a first step may I suggest you write down what you want to do and achieve during your trip. Then I would get a large, wall size map of the US, and start looking at what there is that interests you between those two points. I like the National Geographics map, as it has all the highways, urban centres, as well as National and State Parks, Forests and Monuments. It is readily available in all good map stores.
As you research the places and attractions you identify, place sticky notes on the map. Once you are well into this, you will notice a route laid out before you. You can do your further research through the map centre (on the green bar above) and on the web.
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