How can I change the startup directory of my Terminal on OS X?

I'm not sure if theres a cleaner way, but adding cd path/to/directory in your .bash_profile in your home directory should automatically change your directory to what you specify.

In Terminal.app's preferences, in the "Settings" tab, select the style of your terminal (probably Basic: the default), then go to the "Shell" pane and put cd /any/directory/you/want in the run command box. This will automatically change directory when you open a new terminal.