5101.1 Assessment
Research Question (Clear, unambiguous) "Do student demographics and/or school location affect the quality of arts programming in New York City public schools?" This is both overly general and vague.  It essentially asks if variation might be non-random.  It surely is.
Relevant Literature no discussion of literature
Causal Interpretations (clear, all parts defined, mechanisms, controls, plausible) Well, we would certainly expect schools "with a higher income" can offer more or better arts classes.  Perhaps you meant with higher income students?  What do you mean by diversity and why do you expect it to have an effect beyond economic influences?  In NYC, what does it mean to suggest that proximity to arts institutions could be an alternative influence?  Aren't their art institutions widely dispersed in the city?  
Data (variables, sample, comparison) The table showing the variables that you would like to use against each other seems better thought through than the material preceding it.  However, it is not clear how much of this proposed data will be readily available to you.  
Research Value Well, we have a very long history of accumulating nearly endless data on schools having unequal services and quality of education.  Mainly, this has little effect.  Not obvious why you think this would be different.
Overall Probably the key question to ask here is this: is there anything distinctive about art education.  That is to say, if all you can show is the same pattern that has been shown so repeatedly - schools have resources that are a function of the economic status of their students and so is the quality and variety of education they offer - then this seems a fair research exercise, but potentially a lot of work for low return.  Of course, if the goal is a means to advance in a career around arts and education, then it makes more sense.