Summer Analyst Internship

Hello,

I am currently a junior at a non-target school majoring in Finance and Accounting with a 3.83 GPA. I intend on trying to take the CPA to move into an M&A position at a major bank one day. I'm interning all year at a corporate tax office but am looking to do something closer to banking for the summer. I've emailed smaller IBs in the NY Metro area. Does anyone have any suggestions? Many of the smaller banks mostly say they aren't looking for interns. The alumni from my school mostly only have connections with Big 4 accounting firms -- something I very much wish to avoid at all costs. Thanks for your help.