Here's my suggestion. Pick a local small business that you like, but that could use a better website or web app (something simple, like an appointment scheduler, etc.). More specifically, pick a business that you feel would grow tremendously if only they were more visible online. Pitch a new website for cheap, or even in exchange for goods or services. If they turn you down, don't take it personally, just brush it off and find another potential client.
Now for the good part: measure everything about the current state of their business, from visitors to revenue to ROI on advertising, etc. Build their website, then measure how much your solution improved their numbers.
Make a portfolio with this business as your case study and brag about those numbers. Rinse, repeat.
Don't forget the part about not taking it personally and brushing it off if you get turned down. Good luck.