Effective way to post a Wordpress version of site for development?

Hello I'm developing a new site for a currently live site. I will be moving the hosting away from the asp.net platform hosting that it is currently on and putting it on a shiny new server with wordpress guts. Naturally I want to post the development site to the web so it can be reviewed by relevant parties, bugs can be worked out, and basically polished up before going live. However, the development version of the wordpress site is not totally happy unless it's got it's legitimate domain. currently it's "http://ipaddress/~devsite" and not "http://thefinalurl.com" because of this some resource on the dev site won't map (they don't like the ~ symbol in the address) and the URI and site address need to be "http://ipaddress/~devsite" which seems less than optimal. I've been pondering this dilema and was wondering if I pointed a subdomain of the legitimate url i.e. "dev.therealurl.com" to the development sites ip I could get a more functional version of the development site. If not can you tell me what I can do. A fully functioning site prior to launch is seems more becoming than saying "yes, the site has some broken parts now but it will work once we take it live it'll work... promise" There has got to be a good way to make this happen.

P.S. I'm already building the site on a MAMP setup, what I really want to find a way to make this work on the final production server prior to DNS rerouting.

Thanks a million!