IMHO "staying abroad" is the best form of traveling. You're not going to be steeped into the cultures of others until you live amongst them. Staying at the Hyatt and visiting all the mandatory sights by tour bus is probably the worst and least rewarding traveling experience money can buy.
In college my internships took me all across Canada, staying in each place 4 months at a time. All of those experiences have been invaluable to me, and taught me far more than any sort of vacation I've ever taken.
I certainly agree that it is worthwhile to experience another culture at least once. I am not so sure about more than once, though.