Is there a way to allow a site administrator to have all of the
administrative capabilities available to them without being able to
create new subsites?

In the sharepoint roll-out within my organization, we do not want
our site administrators to be able to open subsites on their own.
This needs to be a centralized process. However, if I create a new
role within a site eliminating the sub-site creation permission, I
still want them to have the ability to manage the permissions within
their site.

This means that if they are smart, they can grant themselves the
capability to create sub-sites. Additionally, creating this
alternative role, eliminates the site administrators access to
several out of the box webparts (e.g. content editor web part, Image
Web part, etc.).