Give us a few more details first, before we can recommend something for you.
What do you currently use with GoDaddy? Shared host or a VPS?
You have high traffic, in combination with a nasty wordpress plugin it can clog up your website.
Do you stream the video out of your site or you embed the videos (like from YouTube or another site?)
Where is your main audience? Is it in America?
Yep, seems like you managed to turn your site into success
It is popular now.
You definitely need a VPS. You can start with a smaller configuration, not to break the bank and see how it works for you and than you will be able to upgrade it as needed.
If you have such high traffic you should be able to monetize from that - so look for ways to make some money from your site, at least enough to cover the running costs.
Selling ad space, google AdSense, etc is usually enough for that.
I'm on a WiredTree VPS and am very happy. I'd pick them if you are ready to go VPS.
About Inmotion: I was actually with Inmotion shared until they kicked me out because of a DDoS attack. For some reason, they did not send me an email that they had taken down my site (reasonably for their protection) until more than 24 hours later when I contacted them about the downtime and waited for several hours for a reply. Other than that affair, I was very happy with Inmotion for four years. One minor problem during these happy times was that Inmotion actually treated me as a usual suspect several times, moving my site to different servers for apparent abuse when they had server problems. But they themselves did some tests later and found that the site was well within resource limits. (These days, I can clearly see with WiredTree's client portal that CPU utilization remains extremely low with our static site.) Inmotion also had several unexplained downtimes with no notification whatsoever.
If you really want to stick to shared hosting. I suggest trying highend shared hosting service like StableHost's Enterprise Hosting. Theirs comes with priority support and most reviews you will find about this host are pretty good. I've never tried them though.