What does the NH regulations state about how long employee time records should be kept? And where should they be kept? Specifically, are time cards required to be maintained at site level? And for how long? Can a corporation with many individual sites centrally locate these records? If so, do these recordbe kept on US soil?

There are many different record retention requirements for different records. For time records, they must be kept for 3 years under the FLSA (NH may require longer, but I don't think so), but I recommend four (some states require four for UI purposes).

You can keep records at any location, but they must be easily retrieveable within a reasonable time frame should an auditor/investigator come to call

N.H. employers must retain a record of hours worked for all its employees except for employees who are exempt under 29 U.S.C. -213(a) of the FLSA, for a period of no less than 4 years. Employers must keep a record of work-connected injuries & diseases for a period of 5 years from the date of injury.