I think the answer is "anything" but who can honestly say, of course any physicist would love to come up with a "Theory of Everything", the next best thing is to unify certain known laws and theories, the building blocks for a TOE. Einstein like a lot of us just had a thirst for understanding, he wanted to know how the universe he was part of worked and what laws applied to it, he was wanting a unified field theory, or "Generalisation of Gravitation Theory".
He was said to be very stubborn so worked towards a unified theory, but he would not listen to a lot of other people, he was dabbling with maths and multiple dimensions, plugging away with numbers like a string theorist.
Not overly much is known about the final years as he became a very solitary sole, a diary of his last girlfriend was found but wasn't very scientific, he did share his science with Schrödinger and I believe if you look about you can find more on that.