Much of what you learn in Ng's course is how to implement these algorithms - there's less (no?) emphasis on using existing libraries in R or Python. I think that implementing your own code base for logistic regression, neural net, random forest, and so forth is an extremely valuable exercise, but I'd recommend you put that aside just for the moment. Instead, try using some of the existing libraries.
For instance, use scikit-learn's logistic regression, neural net, and random forest (not covered in Ng's class) libraries to do a classification. You don't want to use these with no understanding of how they work, but you've done the coursera, so see if you can use your knowledge of how these algorithms differ to create dataset that will highlight the benefits each approach (i.e.., can you create a dataset that works great for logistic regression but poorly for neural nets, or random forest?) Think about how you'd use an unsupervised approach to classification, and run it through k-means. I really think that applying different techniques to the same dataset, on a high level, combined with general knowledge of what's going on under the hood, can be a great way to understand how/when to use these algorithms.