The closest city to the Bárðarbunga volcano is Akureyri, located in northern Iceland. However, it's important to note that:

* Akureyri is still quite far from the volcano: It's about 150 km (93 miles) away from the volcano's caldera, which is located in the Vatnajökull glacier.

* There are smaller towns closer: There are smaller towns and villages closer to the volcano, like Mývatn and Egilsstaðir, but Akureyri is the largest city nearby.

While Akureyri is a significant distance from the volcano, it's still a good starting point for exploring the surrounding areas and potentially witnessing the volcano's activity, particularly if you're interested in the scenic views and geological features.