By global standards, western Europe and the US are quite culturally similar. If you are looking for a larger change in cultures, I would steer away from western Europe. Go a thousand miles further and check out eastern Europe. India, which as many have said could be ideal for a vegetarian family, is much more culturally different from the US than anywhere in Europe is.
But that's if you actually interact within the culture. Nearly every large city around the world has a group of US ex-pats who don't want to go back to the US but don't want to immerse themselves where they are, either. If you wanted to, you could make those people your primary friends and acquaintances. Generally, people go where they have connections, which makes sense, but it can also mean getting introduced only to people who are really little different than them.
Q: How many poets does it take to change a light bulb? A: 1001...one to change the bulb, 1000 to say it's already been done.