What's the must-see thing in Innsbruck?

The Hofkirche sits on Universitätsstraße, a 3-minute walk south from the Golden Roof. Maximilian I commissioned it in the early 1500s as his own memorial, though he never ended up buried here. The tomb is empty. What fills the nave instead are 28 bronze statues, each between 2 and 2.5 metres tall, lined up along both sides of the aisle like a frozen court procession. Locals have called them the Schwarze Mander for centuries. Some of the faces are real historical portraits. King Arthur of England is among them, which seems unlikely, but the Habsburgs traced their lineage to everyone. The bronze has a cool, slightly greasy feel if you touch the bases (you're not supposed to, but people do). The whole visit takes 25 to 30 minutes. Go before 10am when the stone floor still holds the night's cold and the nave smells of beeswax and old wood.

The Golden Roof on Herzog-Friedrich-Straße is smaller than every photo suggests. The balcony is about 3 metres wide, covered with 2,657 fire-gilt copper tiles that Maximilian I added around 1500 so he could watch tournaments in the square below. You'll see it in 5 minutes. That said, the Altstadt around it is where your morning works best. The narrow streets between Herzog-Friedrich-Straße and the Inn River stay in shadow until about 10am in summer, keeping the air noticeably cooler than the open squares south of the Triumphpforte. The smell of fresh bread from the bakeries on Kiebachgasse hits you from half a block away. The Ottoburg at Herzog-Friedrich-Straße 1, built into a 15th-century tower, serves Tiroler Gröstl for around €16. It's a pan-fried hash of potatoes, beef, and onion topped with a fried egg. That's the dish to try on your first morning in Innsbruck.

For the third pick, ride the Nordkette cable car from the Hungerburgbahn Congress station near the Hofgarten to Hafelekar at 2,334 metres. Zaha Hadid designed the four lower stations in 2007, and the full ascent takes about 20 minutes. The round trip runs roughly €39. At the summit in late June the temperature drops to around 8°C even when the city sits at 22°C below. The wind carries the sharp mineral smell of limestone, and the silence after the Altstadt foot traffic is startling. You can see down the Stubaital to the south and the Karwendel range fills the northern horizon. Mind you, the cable car closes in bad weather without much warning, so check conditions that morning. If clouds sit below 2,000 metres, skip Hafelekar and visit Ambras Castle instead, about 3 kilometres southeast. It holds the Habsburg portrait collection and a 16th-century Wunderkammer with its original display cabinets.

For a first day, start at the Hofkirche at 9am, walk north to the Golden Roof and the Altstadt, eat Tiroler Gröstl at the Ottoburg by 11:30, then take the Nordkette after lunch when valley thermals have settled and summit visibility tends to be clearest. The Innsbruck Card (around €47 for 24 hours) covers all three cable car stages, the Hofkirche admission, and most museums. It pays for itself with one Nordkette round trip. One honest note on Swarovski Crystal Worlds in Wattens, 15 kilometres east. It opened in 1995 and appears on every tourist list. It is a corporate brand experience with mirrored rooms and a gift shop the size of a department store. If you have a single day in Innsbruck, the 6-hour loop from the Hofkirche through the Altstadt to the 2,334-metre Hafelekar summit covers 500 years and 2,300 vertical metres of what makes this city different from anywhere else in Austria.