In some cases there is longer layover in Rome and could be a great solution to visit this beautiful city on your way to America. In case of booking please look for flights departing from Germany till 10th of July or from 18th of August 2015 till end of January 2016. As there is long layover in Rome on your return flight this also gives you an option to end your trip there and not to continue to Germany.
Booking sample
Berlin - Chicago for €361
Berlin - New York and Chicago - Berlin for €439
Travel dates are the easiest to check here using +- 3 days searching tool.
To check your connection possibilities from your hometown we recommend to use Skyscanner tool. If you are looking for some affordable accommodation in USA please use this tool.
Booking sample of cheap flights to Chicago from Germany in summer 2015 for €361 here. In this case you would be departing from Berlin to Chicago on 7th of July. Your return flight from USA back to Germany would be then on 23rd of July 2015.