I do not play even CLOSE to visitor's level, but for every new piece, I try to analyze the music: - the modulations? if a section repeats but with differences, what are the differences and how should they be interpreted? I do not write in every chord on the score. In addition, I find it helpful to read about the composer and the period of life the piece was written... has there been any references to how he saw the music? As an example, I have just reasonably polished Debussy's Arabesque, and found references to how Debussy viewed the two hands as a convergence of nature, how he views rubato. It really helped in in the way I interpreted and (I hope), played it. I've done the same with his Sunken Cathedral. Let your fingers do the walking on the internet and you will find a wealth of material that can supplement your weaknesses in analysis and theory. Don't know if this will help you or not.. but a thought.