In a one-man project (webpages or desktop applications) where you're both the designer and the developer, what is better to do first, design or write code?
By interface I am guessing you mean the user interface, as opposed to an API. I always design the interface first. When I'm coding I'm lazy -- I do whatever will get the job done with the least effort. This leads to interfaces that don't make any sense just because that was the easiest (or cleanest) way to do it in the code. But before you have written the code, you are unbiased and will make better decisions about what a good interface will be.
However -- they will still be bad decisions. You may think you know what feels natural, but you don't. Test it on people! Watch what they do, how they try to use your software, ask them questions and adapt accordingly. If you are doing this often, then it doesn't matter if you design first or code first. This is the way to make a top-notch product.