To answer that immortal question “How much traffic does X website get?” we turn to Alexa, the web information site.
A funky graph of their traffic rank:-

They show steadyish growth up until the start of the year, then spikes and declinishness.
But what does that mean? Is it good? How does it compare? What to compare it to?
Well, when I first heard about SongKick, it was explained me as last.fm but for gigs. Last.fm is a well established site, its been around for years now, and how does SongKick compare?

Bah, they’re a couple of orders of magnitude out.
So what can we compare the site to? Well, its a music website, based in the UK, as it Drowned In Sound. Alexa brings forth this graph:-
They match up quite well, SongKick as the challenger leaping ahead occasionally before slinking back. But broadly they have the same traffic rank according to Alexa.
There are of course other webtrafficy websites out there. WebTrafficAgents for example. They have actual pageview and hits figures:-
Daily Unique Visitors: 12,655
Daily Page Impressions: 137,562
Indeed, and how do Web Traffic Agents reckon that compares to DiS? Well their figures are:-
Daily Unique Visitors: 17,866
Daily Page Impressions: 66,697
Hmm, I know, DiS gets more different people, but SongKick viewers click around the site a lot more.