Well, in that case, in the next year learn by doing what you want to do i.e. web development. You still would benefit going through the exercises. At the very least, go through Google's Python tutorial and get some decent coding skills from the MIT intro class (
http://ocw.mit.edu/OcwWeb/Electrical-Engineering-and-Compute...)
After going through that exercise, you should be able to build some non-trivial apps.
For web side, you can benefit from learning at least one web framework (yes, HN folks will flame throw you with framework do's and don't, but for learning sake, just pick one and stick with it). Ruby on Rails is a pretty popular framework and some Ycombinator startups have built extremely impressive sites (scribd, justin.tv, Loopt to name a few).
So, assuming you put in work on the python tutorial or even if you didn't, I highly recommend this online ruby tutorial in 15 minutes. http://tryruby.org/
I'd recommend this Ruby on Rails online tutorial - http://www.railstutorial.org/book#top. It is very new-comer friendly and dips into industry-relevant points that other tutorials don't necessary cover; by that, I mean this tutorial touches base on version control (a program to keep track of what you added or changed in your code) and unit testing (you need this when your code gets ridiculously huge).
And, even though this may sound too early (it's not), look at job boards of places where you may want to work for (this would and should change as your learning progresses). In those places, look at skills required and the tools they use. You'd be surprised how often some jobs care about what you have built and how smart you are rather than your impressive educational credentials (though that can help).