Sure, just sign up for an account on Vimeo, then post a link here. The basic account is free and should be all you need, but I have a paid one which has a lot of other advantages. I suppose you could use YouTube (Guy does), but personally I don't want anything to do with Google's empire. BTW, if there is any copyrighted music in the video - even if it's just playing in the background on a radio - YouTube is very aggressive about deleting it. Vimeo is a bit more relaxed about this, but not much.
Ben has very limited space on his server, and I don't think he wants people hosting their video directly at NJPB, even if it were possible.
You would need a license to use copyrighted music, and even if you have one it can be a big problem. They will pull it down and then you need to convince them to restore it, which can be a huge hassle. You have to be careful, because some companies are selling blanket "licenses" to use music, and then Youtube/Vimeo doesn't recognize them, so you've just wasted your money.
Believe me, I'm a moderator at http://www.dvinfo.net/forum/ and this has been a huge problem for people who do event videography. It's just about impossible to share this on Youtube anymore, and pretty much the same on Vimeo. First, they will just delete the video, but then they have something like a "three strikes and you're out" policy where you get permanently banned.
On a personal level, a week ago my granddaughter created her own Youtube channel and was having a great time making her own dance videos and sharing them with her friends. My daughter sent me a link, and a couple hours later when I tried, the videos were all gone. Now, in some cases, Youtube will pull them and then offer you the option of putting them back up with ads on top of them. But they won't always even do that. And do you really want ads on your video? This has gotten very controversial when political or otherwise offensive ads are inserted on your video, implying that you support those views.
Now, I have a paid Vimeo account and make all my video private. You can still post a link to the private video on a site like NJPB, and you may find that it doesn't get taken down that way. I have shared some video this way and have not had a problem. This article is a couple years old, and it's only gotten worse.
In this week's Talking Tech newsletter, the story of a friend who put Marvin Gaye, Ed Sheeran and others on his video soundtracks and got banned from Vimeo for doing so. Music isn't free, and using someone's material isn't legal online. Consequences come when you get caught.