Many people say that you can't expect to take your kids to a whole heap of museums or they'll be bored.
If you've always done it, it will be normal for them. Whenever you do it, they learn how to behave in such environments (e.g. not touching displays) and it is amazing at just how engaged even very young children can be in galleries and museums.
You generally just have to find something that they can relate to. Read the guidebooks or websites of the attractions and anticipate some things you are likely to see. I once created a treasure hunt booklet for our eldest daughter (then aged 5) so she could find particular things in various New York galleries. She loved it.
The same goes for eating out. If your kids do it from a young age, they will know what is expected and behave accordingly. Encourage, but don't force, your kids to eat the local cuisine if they really don't want to. Giving them a bit of your dinner might suffice to broaden their culinary experience - but don't just give in to fast food. We have forever regretted having dinner in McDonald's in Quebec City, despite there being several more-than-adequate kid-friendly eateries across the street. And when in the UK, our eldest daughter survived on a diet almost completely consisting of fries - we shouldn't have allowed that either.
Don't forget that the kids are still kids. Try to find some special treats just for them - a park, a visit to the ice-cream factory, Disneyland, the beach or whatever you find.
Don't expect too much. It's one thing to extend their cultural experiences, but quite another to expect things which are way beyond them.