They've set up a "Fan Mile" that runs through the city's main pedestrian shopping street, featuring Eurovision activities along the route.
The biggest buzz is to be found at the Eurovision Village, where contest performers hold free concerts during the week leading up to the big show.
This afternoon we were lucky enough to catch two acts, fresh from qualifying at last night's first Semi Final - first up, Iceland's Pollaponk (aka the Scandi-Wiggles):
Then, it was time for the main attraction: Sweden's Sanna Nielsen, the lady who's currently running first in the betting to win the whole shebang on Saturday night.
This is Sanna's 7th attempt to represent Sweden, having failed to make it through at the Melodifestivalen selection trials for the previous six years.
So as a result of this, Sanna has a pretty high profile amongst the hardcore Eurovision fans - and it seemed like they all tuned out in Eurovision Village this afternoon to hear her previous Melodifestivalen hits, as well as her 2014 entry Undo.
There's plenty more entertainment lined up for the Eurovision Village over the coming days, including a concert by contest legend Johnny Logan - and if he's singing Hold Me Now (1987 Irish winner) you can bet I'll be there!
