A lot of us take business trips from time to time, and some more than others. Unless I'm on a 2 day business trip on a mundane trip to Atlanta, Minneapolis or Binghamton, I really like to get out and visit the city or the area I'm visiting (ok in Binghamton, I'm going to be on the town, because I used to live there). Let's face it, having all your meals at the Holiday Inn or Hilton where your company's travel department stuck you, or at a nearby chain restaurant is boring and often crappy, when there is usually a lot of local food to try. A bit of research can give you a real local experience, and usually save a few bucks. Also, unless I'm in a city that's really boring and where I've been a lot, there is always a reason to get out and at least have a look around.
I know people who are scared to death about venturing to downtown Memphis after dark. That's baseless unless you are stoned drunk or wander into remote alleys. On the other hand I've been to Karachi, where there is no way I'd wander out of my hotel without an armed escort. But I've traveled all over the world and mostly have been left unmolested. I travel to the Philippines often, and although Manila can be dangerous (or at least daunting) to the uninitiated, a bit of research and a local guide can give you a good evening even on a short trip of a day or 2. Try to get to know a bit about your destination before you go, and ask your business contact for advice.
Travel really does broaden your horizons, so long as you let it. If you travel to Taipei two times a year, eat your meals at the Hyatt, or seek out the nearest Chili's or Outback, and try nothing local, it is your loss. Nothing ticks me off more than people traveling abroad and either expecting everything to be just like home, and when it is not, gets upset that it is not. Foreign travel is eye opening only if you want to see, and I urge all who travel on business to go to your destination with open eyes, if not an open wallet.
My bottom line here is that very few of us get to travel that is paid by our employer, and when you can, it can be a good value to attach some vacation to the tail end of a nice international trip, bring your spouse or significant other along with you, and enjoy the unique place you are visiting.