Do you have today's local newspaper?
gior-NA-le — the 'gi' is a soft 'j' sound as in 'jump'; stress on the second syllable.
Use this to buy a newspaper. Many tabaccherie also function as edicole (newsstands) and stock national and local papers.
'Avete' is second-person plural, politely used in a shop setting. 'Di oggi' (of today) clarifies you want the current edition. Italian newspapers include La Repubblica, Corriere della Sera nationally, and many regional papers like Il Mattino (Naples) or La Nazione (Tuscany).
Il Corriere della Sera, per favore.
The Corriere della Sera, please.
Simply name the newspaper — no verb needed
Avete riviste di cucina?
Do you have cooking magazines?
'Riviste' = magazines; many tobacconists stock a wide range
È arrivato il giornale di stamattina?
Has this morning's paper arrived?
Asking about delivery — Italian papers often arrive late in smaller towns
Italy has a strong tradition of regional newspapers. The tabaccheria/edicola hybrid is central to Italian morning culture — Italians often stop on their way to work to buy a paper and occasionally also a coffee from the nearby bar.