How do I hide my web site's actual location and public IP?

A web site I'm building lives on an Amazon server in San Francisco. I'd prefer that this new site not be traceable back to me or my other Amazon-hosted properties. Ideally I'd like for the DNS <A> record for my site's hostname to point to an IP address in Antarctica or Netherlands or some other exotic place. The server at that location would then proxy to my Amazon server. But to anyone running a WHOIS or tracert, it would appear the site is located in the exotic location. My Amazon site would only accept inbound connections from the proxy -- not from the general public.

I *think* what I need is called a "reverse proxy" but I can't seem to find any service providers. There are tons of proxy providers out there but they're mainly dedicated to protecting the identity of the client, not the server. Where shall I look? Is what I'm describing even possible?

Thanks.

I think CloudFlare does what you have described.

+1 for Cloudflare.

Incapsula or Cloudflare.

Are you talking about this site?
http://media.amctv.com/img/originals/breakingbad/myshout/pinkman_page.html

I use Cloudflare and I'm happy to say it will make your site load faster and protect your site from DDOS attacks.