Museums, especially art museums, have made tons of progress in figuring out what it means to be a museum in the internet-connected world. All significant art museums now have most or all of their collections online, engaging social media strategies, and effective email marketing programs. And all these efforts are all fundamentally content-driven (i.e., they use the art as the draw), serving the mission at the same time they drive visitorship.
I would draw a contrast here between museums, on the one hand, and zoos and aquariums on the other. Zoo and aquarium sites are heavy on marketing–though without always being savvy about fundraising–and usually provide pretty good visitor information. But they do almost nothing to serve their missions online.