Although I'm a bit reluctant to help make a guide about Juventus, the city itself is nice, so I'll help you out there.
I've never flown into Torino, just the train, so I don't know if I can help you in terms of transport or not, though I will say that the Porta Nuova train station, where most of the trains come in, is conveniently located in the city and the public transportation (trams and buses, mostly) can take you pretty much anywhere in the city. Personally I think it is an efficient system that covers a lot of ground, I like it better than many of the other Italian cities I've been to. Unfortunately I cannot remember off the top of my head the important transit lines, but you can find a map at the train station or ask a local. (For those of you non-Italian speakers that would be "Dov'è ___ ?" or "Como arrivo a ____?" - Where is __? and How do I get to?) If I have time tomorrow I can also dig out my old map. I can tell you though that to get to the Stadio Olimpico you have to take the #10 bus south from Porta Susa for a few stops (not quite ten, IIRC, you get off at the Filadelfia stop).
In terms of places to stay, I can't give you any specific recommendations, there is no specific place I return to each time while I am in the city. There are however loads of cheap hotels leftover from the 2006 Winter Olympics (in fact, some of the decorations are still up around the city) so you shouldn't have trouble finding a place to stay, especially in March. Hostel World
is good for finding cheap hotels and hostels, not just in Torino but all over the place. As for eating, again, no specific recommendations, but there are many places to find a bite to eat. There was a great Middle Eastern and pizza place near my hotel last time I was there (this past summer) but I can't remember the name of it, though the neighborhood was west of the Ospedale Maria Vittoria (which is in fact a hospital, but also a good reference point and bus stop). I also read about a place called Eataly in a book not too long ago. Apparently its a place, kind of like a food court, where you can pay a cover and sample many different kinds of foods and drinks from different shops. It sounded pretty cool, but I never got a chance to pay a visit.
As for places to see, I would go see the Superga basilica just outside the city (can be reached using a combination of public transit and a tram, it is located in the hills east of the city across the Po) which provides some great views of the Po Valley, but it might be tricky to see anything in March due to the weather. Check on a day-by-day basis of course. At Superga there is a bit dealing with Grande Torino, as the crash happened there (more on this later) and the tombs of many of the kings of Savoy, which is interesting from a historical perspective. I also enjoy the parks in Turin. The Parco Mario Carrara (also west of the Ospedale Maria Vittoria) is nice, I saw a great music festival there in July with some pretty good bands. There is the La Mandria park northwest of the city which I have only been to once, but it is huge and pretty nice. The downtown area has its share of cool things, the Giardino Reale and the surrounding area bear the influence of the House of Savoy that ruled the area for a long time before the unification of Italy and has a few monuments dealing with unification and later Italian history due to Torino's brief stint as the Italian capital. Of course there is the Mole Antonelliana, which is fantastic stone architechtural work (some good info if you search it on Wikipedia) which now houses the national film museum (well worth checking out if you like film at all) and if you want you can see the Shroud of Turin (supposedly Jesus' burial cloth) at the Duomo di Torino, but that's never really appealed to me.
In terms of football related things to do, even though the fans are coming down for a Juve game, they would do well to learn about Torino as well. There are plenty of things you can check out including a monument to the Grande Torino side at the Superga basilica. (If you don't know anything about the history of Torino FC at least read up on Grande Torino.) The two main stadiums, the Olimpico and the Delle Alpi are nothing to write home about, and the Delle Alpi (nicknamed the Delle Empty) is acutally pretty bad. The Olimpico has some history to it, but what is really worth checking out is the Stadio Filadelfia a few blocks straight east from the Olimpico. It is the old stadium of Torino FC/Torino Calcio and where Grande Torino played in their heyday. It is a very pro-Toro neighborhood and there are many people there who would be willing to talk about Torino, the city and the club (especially if you drop the name of the club first and NOT Juventus). Haven't been to a lot of bars in Turin, but there are some good Toro-affiliated ones there. Who knows, perhaps if Chelsea win you'll get a free drink.
All in all, Torino is a nice city with enough to do if you are visiting a few days for a football match. Of course I always say when in doubt ask a local. I have been there a few times and have relatives elsewhere in Piemonte, but have not lived there myself for an extended period of time. I know ToniSamp lives there, and I think he is the only regular XT poster who does. This does remind me though, I have a bunch of pictures from Torino when I was there this summer that I promised I'd upload but still haven't due to my hard drive crashing. They are somewhere though so I'll see if I can't find them in the next few days and both fulfill my promise and give you a little sense of what Torino is like. Anyways, hope this helps.