Learn how to decouple yourself from specific technologies. Underlying all programming languages is the 'pure' logic of programming itself and the theoretical stuff of computer science.
Things like algorithms and data structures are largely independent of language (although there are some 'exotic' things you can do in many of them).
I would however strongly suggest getting a strong background in cross platform C/C++ code. For a very long time this has been the only really practical way to write properly platform agnostic code and it still is... you'll need a bit of Java to glue it into Android, and a little Objective-C might help with iOS and OS X. It also lots of quirks due to being low-level enough and will give you a better understanding of why x is slow or difficult to implement in the general case rather than in just 'language and platform X'
Also, for the web make sure you understand HTML(5), CSS and JavaScript - aside from server side stuff these three things underpin everything on the web.
JavaScript is not the next big thing - its like a 101 requirement for serious web development imo...
I strongly advice against deeply following the next big thing too - check it out see what it is, learn about it a little, but don't go nuts. There is a chance that you will learn nothing of long term value from investigating it thoroughly.
Knowledge of APIs and standard libraries is something Google can provide for you these days... understanding never will be.
Things like algorithms and data structures are largely independent of language (although there are some 'exotic' things you can do in many of them).
I would however strongly suggest getting a strong background in cross platform C/C++ code. For a very long time this has been the only really practical way to write properly platform agnostic code and it still is... you'll need a bit of Java to glue it into Android, and a little Objective-C might help with iOS and OS X. It also lots of quirks due to being low-level enough and will give you a better understanding of why x is slow or difficult to implement in the general case rather than in just 'language and platform X'
Also, for the web make sure you understand HTML(5), CSS and JavaScript - aside from server side stuff these three things underpin everything on the web.
JavaScript is not the next big thing - its like a 101 requirement for serious web development imo...
I strongly advice against deeply following the next big thing too - check it out see what it is, learn about it a little, but don't go nuts. There is a chance that you will learn nothing of long term value from investigating it thoroughly.
Knowledge of APIs and standard libraries is something Google can provide for you these days... understanding never will be.