Depends how your travels looks like, you can travel living in luxury hotels, spend most of the time with people from your country either by the hotel swimming pool or guided tours or in the museums - or you can be less savy and go a bit "guerilla" with your travels: go a bit off from the typical tourists' paths, see the real local culture (not the one from museums) and real local people - this should be enough to "open up your mind" for different cultures (of course living abroad adds more of that but you can get some essence even if you stay somewhere for only a couple of days.
My current work as a system engineer implementing ERP systems for overseas affiliates, takes me often to work abroad (from Japan, that is) for a few weeks a time. Although I don't have time to do almost any sight-seeing at all, and although they will usually have me stay in more or less high grade hotels (that narrow one's vision, because they are the same, everywhere), it is working together with the local operators and managers, eating together, understanding their work ethic and habits, getting their feedback, pushing it together through the transition period, so when I go back I feel I understand a little bit more about the country from these interactions than from whatever I saw during my limited time off work.
