No, it doesn't have to be yes. If God is a limitless being, by definition, he/she/it cannot be limited, even by him/her/itself. So, yes, there is something God can't do. He can't not be unlimited.

 You don't HAVE to make it a paradox.  Maybe this god just limits itself just a tiny bit 'cuz it feels like it?  Maybe it never feels like it but knows it has the option?  It's like when a cyborg falls in love with a human and to truly share their love the cyborg has to turn human and lose its immortality?  Man I hated Cyborg 2.

I'm not making it a paradox. I'm going by the definition. If you say something is limitless, it can't have limits. That's simple.

Hell, speaking of God as an entity is limiting in and of itself. But I digress.

I understand what you are going for, and you have a point. What if God felt like limiting Himself (I'm going to refer to God as He and such to cut down on typing). Could He?  In a roundabout way. He could create a lesser version of Himself, and through that version, He could experience limits.

That leads to a deeper question. Can God kill itself?

If God created everything and everything is from God, does not God kill itself everyday?

 That would explain Deism!

Anybody here see the Monty Python bit where the news headlines are all:

"God is dead!  ... and he was really short!"

and then the rest of the bit is the whole world laughing at how short God was when they bury his body?

Who the hell revived this stupid topic?

God.

if there is no God where did anything come from?

like it or not what you believe has ZERO effect on reality.... God exists, therefore God exists is philsophical proof, because He is literally the beginning and the end of all