You need to download maps ahead of time only if you won't have phone service in Italy.
Do you have T-Mobile or Sprint? (Are you from the US?) If so, your plan probably includes free international roaming data, meaning you can use maps in Italy for free without downloading them ahead of time. You can use maps just like at home, because your phone will work in Italy without extra cost (except calls would be 20 cents a minute, if you make any). If you have Verizon or AT&T, then your cost would be $10 per day to use the phone - and you'd be charged only for the days that you use it.
In terms of downloading maps ahead of time (in case you won't have phone service in Italy): the only maps I use on my phone are Google Maps, and their "offline" maps work only for driving directions, not walking directions. There may be other map apps that let you download maps ahead of time that will also give you walking directions. You can still get walking directions with Google Maps while on WiFi, at the hotel or a restaurant or something; bring up the map and get directions and then walk away and you'll have good directions until you get there. You can do that (use the phone on WiFi) for free without having phone service in Italy.
You might also want to buy a local Italian SIM card in Italy so you can use the phone there (instead of Verizon, AT&T, etc.) - if so, we can give you tips on that!