Yes, visiting an art gallery or history museum is great for toddlers.
We live in London and are blessed with a huge number of world class free museums and I would say that taking a toddler to a museum is an amazing experience for both parents and toddler. You will be surprised by how rewarding it is for all of you.
We have been taking our daughter to museums since she was 1. At that age she wasn't able to walk for more than a few seconds before having to resort to crawling, but that didn't stop her from being able to wander around while we looked over the exhibit.
Now she is 19 months and absolutely loves museums. She'll wander around and although she doesn't speak much, she will hold her arms up if she wants to be lifted because the exhibit is too high for her to see. We always try to get to the museum for opening so it's at its quietest, so she has the space to herself and is less likely to be tripped over and follow her as she walks from room to room. Even at her age, for the last few months she will wander up to an exhibit and point at it and babble away about it in toddler language, and then wander on to the next thing that interests her. She will do this for literally hours and often we, the parents, get hungry and bored of the museum before she does. Of course sometimes she's more interested in a sign on the wall or a random mark on the floor than the real exhibit but most the time she 'gets' what it is she is supposed to be looking at.
In my experience, what you don't want is exhibitions designed for children. With these they aren't designed for young toddlers and there are often far too many 'bigger' children running around and it can become unpleasant for the toddler.
But in relation to your question about how to balance what you do for you and what you do for the toddler... when on holiday, after spending a long time in the push chair and maybe a long time sitting down at lunch, we will visit a museum specifically as an activity that is for our toddler.
So, to all these people who are saying that museums are boring for toddlers, just try it once and you will see that that is really not the case. Just remember to let your toddler dictate which rooms and exhibits she gets to look at rather than you taking the lead.