I just want to double check this.

Shakespeare's works are public domain, and therefore open to everyone, right? I've read there are exceptions to the 70 year, I just want to be sure before I waste time on something I can't afford the rights to.

Specifically, I'd like to write a rough adaptation of Titus Andronicus. Since it's public domain I'm good to go, right?

yep your are fine. (this same question came up not too long ago) You are free to use anything and everything from whatever Shakespeare script you want.