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 7th of September till 25th of October 2015.
Booking sample
Berlin - Chicago for €395
Berlin - New York and Chicago - Berlin for €454
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 €395 here. In this case you would be departing from Berlin to Chicago on 10th of July. Your return flight from USA back to Germany would be then on 21st of July 2015.