... but I am going to tell you that remaining at the same university you got your undergrad in is a mistake....
I have to disagree with you on this in some cases (specifically applied technical areas like engineering). If you went to a specific school for undergrad and intend to continue for graduate school, the people you have met and made connections with in undergraduate will help immensely. If you personally know professors that are working in areas you are interested in, picking them as your advisor is one of the fastest ways to get on the road to publication. Also, by actually being at the school you can talk to people who have specific advisors and determine which professors are best for what. (Some professors will support every decision you make, regardless how bad it is. Other professors will disregard every suggestion you make, regardless of how smart it is. You want either the middleground, or two professors (one to make ideas with, the other to shoot them down).
Finally, the best part: If you went there for undergrad, you know where the funding is, (or can easily find out) as well as which faculty actively don't get along. Believe me, this is a relief.
You knew the job was dangerous when you took it, Fred. -- Superchicken