hi, currently, your academic performance sounds not bad. More importantly for you to get into Harvard/Yale/Princeton is your match, whether you share similiar research interest with the faculty there. Besides, you need to convince it to your committee through a solid personal statement. High GRE would be a bonus for you. As you said that you are doing some research project , if you can turn them out into some publication, I mean academic paper at least, your chances will be much higher! Last but not least, delve deeper to more programmes which match your interest, I think it is good for you to look around to know the width first and then decide where to go.