Web crawling app
A web crawler is an interesting project, which can show your web skills, and also shows that you are interested in doing something more than just some basic applications. So you can do one of two things: you can build a website that uses the scraped information for some purpose or you can automate the scraping program to do something with that information on its own (for example, scraping the news and posting the top 3 articles on your social media feed).
Skills you can show: automation, web development, web scraping, database management
An app that integrates third party APIs
An app that integrates third-party APIs shows that you have extended knowledge in using other tools to achieve a bigger goal. For example, you can try with Google APIs - they are easy to use and offer free options to try out. You can integrate maps, places search, or even chat, Gmail, etc.
Skills you can show: API access, research, finding tools that can improve and make your solution more advanced

Bots
Bots are always fun to play with, and even more, fun to develop. You can use some existing solutions to implement your own bot, like for example Twilio. Twilio is an API for text messages and phone calls. Make a bot you can call that will tell a joke.
Skills you can show: API access, innovation for fun projects
Expansion options: Connect it to TODO list, Connect to GitHub Notifier, Connect to Weather App
Image or pdf editor
You can create some basic image editor, that will do something like meme generating, and, for example, will put text on an image the user uploads. Or if you want something more advanced you can programmatically edit the text in a pdf file the user uploads. This will show you know how to work with files and programmatically modify them.
Skills you can show: Graphics, file I/O
Expansion options: Preview, GUI, Text parsing

Progressive Web Applications
Progressive Web Apps (PWA) are front-end applications that can be used natively on many platforms, including installing them from the browser on a mobile device. This type of app can show your interest and knowledge in multi-platform apps, and while developing one, you will surely learn something new!
Skills you can show: Multi-platform development
Games
Developing a certain type of game can show different skills you possess, and make your recruiter interested in them. For example, depending on the job description, you can choose a game where you will implement your knowledge in graphics, artificial intelligence, web development, mobile apps, or even desktop apps. You can show your design skills, problem-solving skills, and also your innovation skills.
Skills you can show: Various skills, depending on the job description you are applying for.