When you say America do you mean USA or other countries in N. America as well?
If you plan to stay in USA, there will be tons to see and do in California. The other States around California (such as Arizona and Nevada) will have loads to see as well. It is very likely you will meet up with other travellers if you stick to LA, San Fran, Las Vegas, Grand Canyon etc.
On the east coast you can go to New York City, Washington DC, and all around Virginia and Maryland. You will notice alot more US History in those places. You will meet up with other travellers there as well.
If you want to see the Rockies would you consider going into Canada. The Canadian Rockies between Banff and Jasper are incredible. On the east coast of Canada, St John's Newfoundland would perhaps be one of your most memorable travel experiences ever.
It is perfectly safe travelling almost anywhere in North America with the proper percautions you would use anywhere. Stay away from Detriot and other industrial based cities. There is no need to go there and there are some bad pockets.