I've never been to BM, but I think there are many art/music festivals which you could go to that are more accessible and very similar themes and things happening burning man has, but on a smaller scale. I just attended my first "art/music" focused festival a few weeks ago. It had meditation/yoga/various educational workshops, artists displaying all different kinds of wares for sale, people trading and giving small things freely (think shared water, wristbands, food, trinket). There was a rock that had a sign, purposed to "give something, take something". The downsides were there too. Lots of people just there for the music/drugs/party aspect or whatever. There are probably 100's of alternatives to burning man - regional burns and music/art festivals, that are much more accessible to get to and experience. Most are 2-3 days long, and that is more like prepping for a regular camping trip than something the scale of burning man.
Your question is too vague. What's important to you?
Is it the culture of being totally present, here and now? Well, then you need to find something that without cell phones, computers, etc.
Is it the culture of sharing? Then you should find something that tries to run itself without money.
Is it the art and the spectacle? Find your local arts community. That's probably the easiest.
Find something doing stuff you like to do, go in and participate--even if you are an introvert. There is something very different about standing on the stage than standing behind or beside it.