One of the great things about being in a big city is the choice of museums and galleries available. Actually, I know people who would refuse to go in any gallery regardless of what it is about, but I am sure they are in a minority.
Here in London we have some great places to visit. Some are free. The National Gallery, the British Museum, the Science Museum and the V&A are. If there is a special exhibition on you will probably need to pay and I suggest booking in advance (on line) to avoid disappointment.
For most places there will be security checks and limits on bags that can be carried around.