You should consider coming here with a study abroad program. This will allow you to have a taste of what NH has to offer for a few months without needing to make any long term commitments. I did a quick search, and here are the schools in NH that have study abroad programs:

• New England College
• Keene State College
• University of New Hampshire
• Plymouth State University
• Dartmouth
• Southern New Hampshire University
• Franklin Pierce University
• Granite State College
• Rivier University
• Saint Anselm College
• Manchester Community College (NH)

You can also explore doing an internship in between semesters. There are lots of places that offer internships in NH! Some places that I know of are DEKA, Texas Instruments, BAE Systems, WMUR, Merchants Fleet, VHB, and so many more!

Good luck!