Can you store the luggage until the afternoon?
'Custodire' — stress the third syllable: 'cu-sto-DI-re'. 'Bagagli' — 'ba-GA-gli' with the soft GL sound.
Use on check-out day when you want to keep exploring the city before leaving. Most hotels will store luggage for free for former guests.
'Potete' is the second-person plural of 'potere', addressing the hotel staff collectively. 'Custodire' (to store/guard) is more formal than 'tenere' (to keep). 'Fino al pomeriggio' means 'until the afternoon'.
Potete tenere le valigie fino alle sei?
Can you keep the suitcases until six?
Uses 'valigie' (suitcases) and a specific time
C'è un deposito bagagli qui?
Is there a luggage storage here?
Asks about the existence of a storage facility
Lascio i bagagli alla reception.
I'll leave the luggage at reception.
States your intention rather than asking permission
Luggage storage (deposito bagagli) is a standard and free service at Italian hotels for guests checking out. Many train stations and tourist areas also have paid luggage storage services run by companies like Stasher or Radical Storage.