Graz is a town, some say city (depending on your definition) you might not expect to exist in the German-speaking world. It may have something to do with the fact, that you have never heard of a city called Graz to exist.
With its well-preserved old town from the Middle Ages (UNESCO World Cultural Heritage), a castle hill in the center, many colorful, well restored buildings of more than 100 years old, day and night safety for Western standards, and super-safety for world standards, Graz is a true treasure chest in many ways.
As for mentality and geography I would say Graz is the most southern of the German-speaking cities above 300.000 citizens.
Graz is highly educated, some say uber-educated, since it's Austria's city with the most academics per inhabitants due to several universities and colleges with up to 80.000 students.
Graz is associated with names such as Johannes Kepler (astronomer), Nikola Tesla (inventor), Friedrich Mohs (mineralogist), Arnold Schwarzenegger (actor/politician), Frank Stronach (MAGNA Automotive), Dietrich Mateschitz (Red Bull founder). Those were either born and raised, had studied or taught in Graz, but all of them had to leave Graz to become big, since Graz still hasn't the capacity to provide the right environment for such talents.
Graz is definitely not perfect. It's not edgy nor cosmopolitan, since it's just not big enough for being edgy, nor is something revolutionary to be expected from Graz or being early adopted in Graz, despite the exceptions. Having said that I would say Graz is on the edge, on the edge of the Balkans.
As for the weather, Graz is hard to compete with, since embedded in rolling hills at the southern foothills of the Alps, protected from harsh weather systems and strong winds from the Atlantic. Normally there is no wind in Graz at all or at best a wind not noteworthy. So normally Graz is also cosy in the winter and ideal for chilling all year-long. Therefore in the days of the Austrian-Empire (Habsburg Empire) the wealthy seniors chose Graz as their place to retire. This got Graz the nickname "Pensionopolis".
Even during the winter you can sit in a cafè's patio soaking up the sun, which Graz has plenty of, since it has the most sunshine hours of any big city in the German-speaking world. Graz is blessed with mild Mediterranean climate it shares with northern Italy and the Balkans.
Some say Graz is already part of the northern Balkans. Others strongly object this notion and argue that Graz is the most southern big city of the German-speaking world.
All this makes Graz aesthetic, sophisticated, and as a city the most southern German-speaking outpost, located in the south of the Alps at the frontier of the German-speaking world, just like Miami or more so Key West for the USA as their most southern outposts, located on the edge of the Caribbean, participating on its mild climate and relaxed vibe.
One final hint: If you are into hurricanes, seaside, notoriously muggy weather, and crime, I suggest to stick with Miami or Key West, because Graz isn't known for that.
Dr. Dr. Immanuel Fruhmann