We just got home from a wonderful family vacation to Chicago, although the trip was mostly to see family we also took in some of our favorite sights. My favorite place to visit is The Art Institute of Chicago, it's collection is jaw dropping , the facility is beautiful and the staff is helpful.
As with any outing we started the trip with a full belly, a clean diaper and baby girl snuggly in the ergo. My kids love to be worn but if yours are fans of the stroller you are still in luck most museums are stroller/ wheelchair accessible. It also gives your kids a place to sleep if need be, That is what my daughter did more than anything, but while she was awake we had fun with these very simple activities:
1. Big & Little - As we went around the galleries I labeled works of art as large and small to keep her engaged without being disruptive to the other patrons.
2. I Spy - well sorta. My daughter loves dogs and cats and I spent extra time at works of art that had those and other recognizable items quietly encouraging her to point and say the words. For older kids ask them to find a detail that's tricky or semi hidden is a great way to keep them engaged and looking deeper into the works of art.
3. Your pick - with my daughter I stood in the middle of the room and let her get a good look at everything and waited for her to point ( her favorite form of communication at 11 months) and then we'd go in for a closer look. One painting she was so smitten with she started signing more when I turned to leave. I bought a print in the gift shop after. For older kids simply ask which is their favorite in each room. Don't forget to ask why.
We did the above a handful of times before naptime came ... but please don't be shy about exposing your very young kids to art!