I'm a big fan of the Jacobin Calendar/French Revolutionary Calendar ever since I discovered the Jacobin Calendar bot on Twitter. It's a decimal calendar with 12 months of 30 days each, split into 10-day weeks, plus an additional 5 festival days (6 in a leap year). Every day of the year has its own name, mostly associated with plants, animals, minerals, or tools, relevant to the time of year (this replaced the tradition of associating each day with a saint). I've given a version of the calendar at the end of this post.
I've started using this calendar as a basis for time in my games. I've made some small adjustments (the French year starts in mid-September; mine starts in mid-March, as the world re-awakens after winter). The day names are great for adding flavour, and for determining events or theming adventures at that time of year. There is no reason why you couldn't rename some of the days (or all of them, if you can be bothered) after something specific to your campaign. How about a calendar of monsters?
The ten days of the week are simply named according to their number - so first day (primidi), second day (duodi), third day (tridi), etc. Again, these could easily be renamed.
All of the festival days take place in late September - harvest time. Again there's no reason why you couldn't move these, perhaps spreading them throughout the year. And you'll no doubt want to rename "Celebration of Revolution" if playing in a feudal or monarchist setting!
Here's the calendar...
