Bars, like restaurants, are non-smoking.
Italians enjoy going out during the evenings, so it's common to have a drink in a bar before dinner. It is called Aperitivo. Within the last couple years, started by Milan, a lot of bars have started offering fixed-price cocktails at aperitivo hours (18 - 21) with a free, and often a very good, buffet meal. It's now widely considered stylish to have this kind of aperitivo (called Happy Hour) instead of a structured meal before going out to dance or whatever.
While safe to drink, the tap water in some peninsular parts of Italy can be cloudy with a slight off taste. Most Italians prefer bottled water, which is served in restaurants. Make sure you let the waiter/waitress know you want regular water (acqua rubinetto) or else you could get water with either natural gas or with added carbonation (frizzante).
Rome, in particular, has exceptional pride in the quality of its water. This goes right back to the building of aqueducts channeling pure mountain water to all the citizens of Rome during Roman times. Don't waste plastic bottles. You can refill your drinking containers and bottles at any of the constant running taps and fountains dotted around the city, safe in the knowledge that you are getting excellent quality cool spring water - try it!