Can you give me a map of the city?
'Cartina' — stress the second syllable: 'car-TI-na'. It is the diminutive of 'carta' (map/paper).
Ask at the concierge or reception desk upon arrival. Most hotels provide free city maps, and the concierge can mark points of interest for you.
'Mi può dare' = 'Can you give me'. This combines 'mi' (indirect object: to me), 'può' (can, third person singular), and 'dare' (to give). 'Cartina' is the standard word for a small map; 'mappa' is also used and understood.
Avete una mappa del centro storico?
Do you have a map of the historic center?
Uses 'mappa' and specifies the area
Può segnarmi i punti di interesse sulla cartina?
Can you mark the points of interest on the map?
Asks the concierge to annotate the map
C'è una cartina degli autobus?
Is there a bus map?
Requests a transport map specifically
Italian concierges love to help with directions and will often draw on the map or highlight a walking route for you. This personal touch is considered part of the service, not an imposition.