There are different types of symposiums out there, but I'm focusing on educational events - ones with a selection of classes over several days taught by instructors from beyond the local area. This is quite different from your paddlefest type of events, where an outfitter, or group of outfitters, have a bunch of demo boats and run people through short clinics or discussions. Those can be valuable too, but they're not the focus of this discussion.
The most obvious benefit of taking classes are the things you'll learn in those classes. I'll just assume that people agree that learning in a class can be valuable (though it's fine to learn through other means as well). But you could probably take the classes through your local retailer, or find a private instructor, or just a skilled mentor willing to guide you. You could often do it cheaper, break it up over convenient weekends, and maybe at a closer location. What makes it better at a symposium?
While learning anything takes time, and physical skills in particular take much practice and repetition, there's a certain psychological advantage to immersing yourself in something for an extended period of time. It can be tiring, both physically and mentally, but the blending, combining and reiteration of ideas you get from back to back courses really helps. It will take time after a symposium for the material learned to sink in, but there's an efficiency to getting so much information downloaded at once. It allows you to draw from a bigger base of knowledge when working to improve. It primes you for more learning and lasts longer.
Variety of Instructors
Symposiums tend to bring in some of the most experienced and well-traveled coaches, who not only bring their personal experience with them, but also the experience of all those people they've interacted with in other places and at other symposiums. Again, the more variety the better. It's something that's hard, if not impossible, to find in any one area of the country.
(Another perk is that these folks tend to bring their stories with them, sometimes even a little video. If you want to be inspired, these are the people that can do it)
Variety of Location
Why is it better to learn someplace new? Because learning is about the new - it's about leaving the familiar behind and taking risks, even if it's just a little pride on the line. Venturing into the unknown changes your mental state and that's good - you want to be a little on edge. It forces a sharper eye and focused mind. As long as you're in an appropriate class, you shouldn't be freaked out about conditions or worried unduly about your safety (that shouldn't happen in any class). But a little bit of concern is good.
If the symposium is happening in your back yard, then maybe the venues won't be new in themselves. But there's a good chance you'll get different venues from one day to the next. Again, it's back to the benefit of variety, the chance to put to use what you learned yesterday in a new context today. It's a new way of looking at a familiar place, and that alone is worth a lot.
It might seem like a small thing, and it hopefully won't be an issue at all, but most of the events I've taught at (GGSKS, Lumpy Waters) have great instructor/student ratios. There's often a safety officer and luxuries like motorized boat support that you don't normally get in a kayak class. And it's not uncommon to have additional safety boaters in the more advanced courses. People often push their limits at these symposiums, and the organizers are prepared for it. It doesn't mean you should sign up for things beyond your skill level, but it's nice to know that when you stretch yourself there will be people there to support you.
I know that these symposiums can often seem expensive. It's difficult to take the time off from work, travel to a far off venue, work your body hard for three or more days. And it isn't something you need to do often. But if you've never been to such an event you're missing out. Treat yourself at least once. It's worth it - and you deserve it.