If you are bored with Venice you are surely bored with life. I've been there 5 times and I never find it boring. It's become very overcrowded in the summertime, something of a victim of it's own success but go in the winter when it's cold and foggy and practically deserted and you'll see a totally different city. It's so much easier to get around in winter too, there aren't so many vaporettos but the ones that run are less crowded.
I can't say that there's any one thing that you really should see or one thing you should do, just being there is enough. It shouldn't exist, it's a crazy notion to build a city in the middle of a lagoon, especially 1,500 years ago and then to go on to dominate trade in the eastern Mediterranean but they did it. Venice's fall from grace was equally spectacular and they are now "just" a major tourist destination with all the problems that brings. The locals can get fed up with hoards of tourists and I don't blame them but I've always met nice locals there. It's not for everyone, my friend is a great traveler and supporter of World Heritage and she was unimpressed, I still don't know how, but for most of us it's a magical place that should be on everyone's bucket list.