Vesuvio is a decent place to have a drink. It was a hang out of Jack Kerouac and other beat writers back in the day. http://www.vesuvio.com/ The modern art museum has always had some really cool exhibits when I've visited. Stay away from the downtown district - its mostly corporate and doesn't have much culture outside that. I've spent a decent amount of time in the city and most of my favorite times have just been picking a neighborhood and exploring for a whole day. I typically pick a neighborhood / district to have breakfast and then get recommendations for bars, shops, entertainment, parks, etc... in the immediate vicinity. If you're cool being flexible with your time and not necessarily seeing all the big ticket items (mentioned in a post above) then I highly recommend that route - the city has a ton going on and is one of the most fun I've ever explored. PS. If you're not on train route public transportation is surprisingly weak.