I know it is an RPG, but can it also go under the sandbox game category because it has a vast open world you can explore and have fun without doing the main quest?

yes.

Although its a limited sandbox

Yes.

Yes

If that is your definition of "sandbox game", then yes, that's what Skyrim is.

Skyrim to me, Is neither RPG, Nor Sandbox, it is Skyrim, a self-explanatory masterpiece!

I will say it is IMO a Muddy Sandbox game. It is an open world with some linear and limited options and quests at points.

I usually use "open world" instead of "sandbox," although this has more to do with personal preference rather than some great semantic difference.

Until the Construction Kit is released :3

Which is never. Even then, it's going to be limited.

i'm going with open-world action roleplaying sim.

because it just doesn't fit my rpg definition.

@dontdoit, I agree with your comment whole heartedly.

Sure, it's a sandbox or open world to an extent. But unfortunately, in it's current state too many quests can be broken beyond repair if you go certain places without having the quest stage that tells you to go there and do x, y or z. So to keep from bugging my characters, I'm playing it linear until (hopefully) the big patch coming (soon?) fixes the scripting. (Or the modding community gets the CK and fixes it if the patch don't.)