Are you flying into FCO? The airport does have at least one cell phone store, not sure if it's carrier-specific or an authorized reseller, but google can help you there. You might be able to just get it done before leaving the airport.

Google Maps is updated as far as roads go. It's searching for specific businesses that gets a little hairy - for instance, search for supermarket/supermercato in Florence and the results are not that good. I just did regular google searches for those, noted the address, and then mapped the address in Google Maps. But yeah, it's fine for navigation.

For public transport within the city, I didn't use any of that, we mostly walked. To get between cities, I just use the Trenitalia website to book trains - the Frecciarossa between Rome/Florence is nice.

Tripadvisor is a good app if you have a live data connection. They also have Tripadvisor City Guides as a standalone app with offline content - they have specific apps for Florence and Rome at least. I'd download both, nice to have.

Otherwise, how is your Italian? Specifically for food, I trust 2spaghi and yelp.it more than I do Tripadvisor. Tripadvisor is written mostly by tourists, and when you're a tourist, everything is magical. 2spaghi is almost 100% Italian, and yelp.it is mostly as well. Not sure if they have country-specific apps, but they do have mobile websites.