Hi Leigh,
Check out some of the lessons on Learn ArcGIS. Here is a filtered view that might have some things that are relevant to you: https://learn.arcgis.com/en/gallery/#?t=lesson&c=spatialanalysis
These are all step-by-step tutorials but going through them should give you some ideas of projects you can take on, and will also introduce you to datasets that you can adapt to a similar workflow to build up your portfolio.
Without knowing what kind of analytical projects you have in mind, I'll recommend a few here:
Investigate Pollution Patterns with Space-Time Analysis
Estimate Solar Power Potential
Determine How Location Impacts Interest Rates
Analyze Urban Heat Using Kriging
Explore NOAA's Deep-Sea Coral Database
If you're not familiar with Living Atlas, you should check it out, because you can find lots of really useful data there. The lesson Get Started with ArcGIS Living Atlas of the World is an introduction to the different resources available with Living Atlas and the different ways they can be accessed and put to use.
