If you really are a 20 year old my guess is your priorities would include meeting european women and night-life. You options for these two will be exteremely limited based on this itinerary. I would focus on Amsterdam and Ibiza in Spain. Barcelona would make for a good stopover - fly low cost ams-bcn and take a ferry over to Ibiza town - or get a one week package deal in Ams (cheap and easy). Save Italy for when your already hooked up - It's expensive as hell and the night-life in Italy is nothing to write home about.