Make your own spam filter/email category sorter, tailored to the types of emails you want to prioritize
Do a deep dive into solutions for a specific NLP task (summarization, translation, speech synthesis, etc.) and analyze where each solution does well or falls short
Do a deep dive into the types of problems that a specific model can solve (CNNs, RNNs, BERT, etc.) and analyze where the model performs well or does poorly
Make a browser extension that mimics Gmail's "smart compose" feature, but in any text field
Fine-tune a generative model (e.g. GPT-2) and write a short story with its help -- analyze what the model does well