1. Local transport is pretty convenient thanks to a wide network of buses, trams and metros. Tickets are the same for buses and metros; and are sold at major railway stations, airports and tobacconists. Yes, unlike in our country, it isn't usually sold on the bus. You have to buy the ticket in advance and punch it in the bus, to avoid any fine.
2. Tickets are usually valid for 80-90 mins after punching, so you can always buy stubs in advance and punch them as required.
3. Buses, metros and trains run as per fixed schedules and are pretty bang on time. So you can simply google a route to plan your travel. You'll get everything from the route to bus & train numbers and travel time.
4. Some of the cities have tourist passes for 2-3 days, that can be used across local transportation. Unless you intend on using local transport extensively, the passes will work out to be pretty expensive. You'll be better off buying tickets (Or walking, if you really want to enjoy).
5. Most of the shops shut around 6.30 - 7. If you want to explore the local markets in Florence and Venice, best do it earlier in the day.
6. Tap/fountain water is usually potable. Just carry an empty bottle and fill it wherever you can. Water isn't given separately in restaurants or hotels (Don't expect those two complimentary bottles in your room either). If you want to take the safer route and stick to bottled water, buy it at a departmental store. (You'll save a lot, trust me!)
7. Most restaurants across Italy have a mandatory cover charge per person. Some also insist that they'll serve you, only if you order drinks. May sound absurd to us, but that's their way of life. Also, do not directly go and sit in the local restaurants. Always advisable to ask if they have a table and allow them to spell out any incremental rules.
8. If you are a vegeterian or vegan, a margherita pizza or cheese pasta will be your best friend in Italia. You'll find limited vegetarian options in restaurants. However, street stalls have plenty of knick - knacks that you can make a meal out of. You can also find Indian restaurants or fast food chains like McDonalds. But, these are scarce and may involve a bit of travel.
9. Hotels charge a city tax (per person, per night). The amount depends on the star rating of the hotel. Factor that when you are budgeting your trip.