How do I BEST spend my next 2 Months Before an Internship Application?

While I understand the application process for summer has started for many companies (I'm also open to a co-op), I want to give some context…

I transferred into computer science my junior year (currently a senior) and I feel very behind. Although I have been accepted into my uni's accelerated masters program I want to get a nice companies internship under my belt.

I grew up out west and love to travel – Currently on the east coast, I'd love to have an internship experience the company would pay for my housing and get something great on my resume!

I have an idea for a web application, it would be my first real side project… But since I'm inexperienced, it's probably going to take a while to create.

For someone that feels inadequate, please tell me how I can best spend my time to get a great software internship!