Where they live, now or later, is less of a problem than what they experience.
Travel can provide a good exposure, or a limited one - it depends on how you do it. But understanding the rich fabric of the community in which you live is more important. Look into the various festivals that occur within a 2-hour drive of your home. In our area, within an hour's drive, there are Italian festivals, Celebrate Israel Day, Armenian festivals, Latino programs (and not just the bar serving margaritas on Cinco de Mayo….), Greek cultural programs, the India Society open house, and many more.
There are a million restaurants of every nationality and I agree it's great to try many of them. That doesn't mean ordering Chinese take-out which is often Americanized versions that would be unrecognizable to people who really live in that area.
Get DVDs from the library - National Geographic covers many things beyond lions and marine iguanas. Get out the world map, figure out how people might travel to those countries. (Kids today, and many adults, think you just set the GPS and you arrive - but look at how people really travel, where ships would dock, etc.)
Remember that you can't always see the differences in people. What people "appear" to be is not always what they are.
I was teaching Spanish in a Jewish day school, with kids born in the US, Israel, Russia, Tajikistan, etc. For many, it was the 3rd language and sometimes the 4th. I took them to a Latino market (with prearrangement with the store owner) and did a scavenger hunt with them - just having to find foods from different parts of the world or surprising animals (e.g. canned octopus) was an education, but in a fun way). We then went to a Latino service center to learn about the countries that funneled new Americans to this area, saw the food pantry (we collected donations), learned about the furniture and housewares pantry and the clothing pantry as well.
The school did a year-long cultural arts celebration with food, music, history, dance, art and crafts and other aspects of different cultures within different parts of the world. Our local public school (grades 4-6) does a major world cultures unit with exhibits and food, plus kids dressing in clothes from a different culture - not necessarily their own (and frequently not). Encourage your children's school to do something similar.
Discuss current events in an age-appropriate way. For example, there was so much hoopla and negativity surrounding children crossing our southern borders, with the buses being blockaded by chants of "English only" and "go home!" Discuss with your children why people come to this country and how - 400 years ago, 100 years ago, 5 years ago. How do they travel, and why? What's involved in the decision to leave your homeland? What happens once they get here?
Museums are great resources - whether it's art or history or environmental science/climate change, we're all part of the world community where these issues are concerned.
Move beyond national origin to achievements by other communities: the ADA requiring companies and municipalities to make buildings and sidewalks accessible, stores and restaurants being required to admit service animals for all kinds of issues (blindness to war vets with PTSD), mainstreamed classrooms for those with developmental disabilities (there are probably quite a few people employed at your local stores who would have been marginalized or isolated 20 years ago), pressure to dress/act "like a boy" or "like a girl" and what that means (from blue/pink nurseries to gender-speicifc toy aisles to schools not allowing gay kids to go to prom, or the recent valedictorian speech shut down by the administration because the boy came out as gay), religious differences (think about the Christmas music that starts in October or the debate about not being allowed to say "Happy Holidays", whether schools close on other holidays and what that means for students and staff) and many more examples of daily tolerance that should, but often don't, occur.
If you can host an exchange student for anywhere from 3 weeks to a school year, do it. We have lots of summer programs that bring students (often with limited English) into the community for a few weeks. It's not a financial stretch for most families to help out in these.
Do your family tree through Ancestry.com if you can. I have a very detailed one from my great-uncle (it's a several hundred page published volume that he compiled in the days before the internet) but now it's easier.
Have them learn a language! While there is value in any language study, I think at least one should be a language that is commonly spoken in your area. I studied Spanish and have used it for decades, from reading store signs to speaking with grandmothers whose 5 year old grandchildren are trying to translate for them with a cashier, to working in medical and nutritional settings. Watch kids' shows that feature another language.
Look into the rich native American tradition and history of your area. There's not an area of the US that didn't once belong to someone else, so for kids to realize that their own neighborhood wasn't always white and English-speaking can be very enlightening.