Haven't had a chance to get to Tanya yet. I have played some other matchups for extended periods against good players and have some early opinions. None of this is set in stone and I'm not an authority on any of these, just a very early and simple assessment based on my own experiences playing offline against good players.
Mileena (All) - Even, maybe slightly in Goro's favor. She's pretty easy to block and doesn't have the scary 50/50 of other chars. And her specials are hella unsafe.
Kitana (All) - Very bad for Goro. Fans shut down his moveset. Assassin and Storm are terrible but Mournful is manageable, maybe even
Cassie - Slightly Cassie's favor in Spec Ops. Her whiff punishes are really good and zoning is a bit annoying for Goro. Also has a very good jumping punch. Not a lot of Hollywood exp but Brawler seems better, closer to even.
Kung Lao (Tempest) - Bad for Goro. Lao gets great pressure since he has a string (forget which one, its with the flurry punches) that can cancel into hat and is uninterruptable. So he pretty much gets free throws. Teleport is also a little annoying since Goro's d2 is ass and spin blows up stomp so his zoning can be a pain
Kano (Commando, Cybernetic) - Commando is slightly Kano favor and Cybernetic is bad for Goro. In Commando, Kano can blow up pokes into PW so you can't play as mindless against him. In Cyber, you don't really have to worry about mixups but when he gets his zoning started its very hard.
Sub Zero - Fairly even or slightly Goro's favor. Not bad if you can manage to stay out of the corner. EX PW and ground pound eat ice klone and force Sub to approach, which is what Goro wants. He has a decent 50/50 game so it can still be hard if you get caught w/o meter. On the other end of the spectrum, if you have a bar and have a healthy life lead, things can get grim for Sub as his approach gets shut down on reaction with EX PW or EX stomp.