I don't think it has to be a binary choice: "If this is Tuesday, this must be Belgium" trips or mini-residencies. True, if all one does is stay at the hotels that cater to travelers and eat at McDonald's and the Hard Rock Café and just gaze at the major sites from afar, a "life-changing" experience likely is not in the offing. But one can be in a country even briefly and get more of a feeling for it than you could from a coffee-table book or Trip Advisor.
I still remember very clearly my first visit outside the U.S., to Japan. I remember going through the clouds as we descended, seeing all the lights and signs in a language I did not know, and, for the first time in my life, lining up at immigration under the sign marked "Aliens". I remember visiting a restaurant there for dinner and not knowing any of the local customs. I remember figuring out the Japanese train system so we could visit Tokyo, even for just a few hours, and walking the streets of Akihabara and the Ginza and realizing that the Shiseido store looked just like Macy's back home. That wasn't a long trip at all but it was long enough to leave a deep impression that reading books and Web sites would never have given me.
I think the key is to get off the highly-beaten track and talk to people. On our recent cruise, people got off the ship, got on the cruise-chartered bus, and went to Blarney Castle. We got off the ship and wandered through the part of town by the port; admittedly not deep into Ireland, but we walked through grocery stores and sat at a coffee shop and listened to nearby conversations and talked to shopkeepers. Great insight into a culture? No, but at least a little, and nothing the Blarney tourers ever got to see.