From a draft of Lawrence Trask’s Etymological Dictionary of Basque, with abbreviations expanded by me:
hiri (Labourdin, Bas-Navarre), hí(r)i (Souletin), iri (Alta Navarra, Salazar, Roncalese), uri (Vizcayan, Gipuzkoan) noun ‘town’. 1545 (but see below).
From *ili, of unknown origin, by rhotacism of /l/. Last form by Bizkaian /i/-backing. The Romans reported a town called Iliberris in south-central Spain, and this name looks remarkably like a Basque formation meaning ‘new town’ (berri ‘new’). But there is no other evidence for Basque speech so far south, and we must suppose either coincidence or an undocumented settlement in this area by Basque emigrants. A second Iliberris (modern Elna) is recorded in Rosselló (Pyrénées-Orientales) (Coromines 1995 s.v. Elna), [...] The form (h)uri is well recorded from the 11th century onward in the toponymy of Alava and the Rioja, while iri is equally well recorded from the 11th century in Navarra.
If you're willing to consider outright speculation, it's worth mentioning Sorin Paliga’s Urbian theory. According to this theory, there is a pre-Indo-European root *ol- / *ul- / *or- / *ur-, connected with the concept of a town, present in this Basque word, Latin urbs, the name of the Swiss city of Uri, the name of the Iraqi city of Erbil, Greek labyrinthos and several other words.