Hmmmm if you're at this stage, I recommend going to Open Data and Civic Hacking meetups. At least in Chicago I've been finding a very high ratio of important problems to technologists who are willing to tackle them. You'll have a blast, meet lots of interesting people, and actually do something that contributes to general welfare :).

Since these problems are so applied and the datasets can be varied, you would definitely not be at a loss for "large and difficult".