There are two which have a Michelin star: Battebecco which is on the square and Bitone which is about two miles from the center of the city. Bitone has more style and has a great chef/owner who is very good at making everyone in his dining room feel special. Overall, however, Battebecco is slightly better for food. Bitone is the more "rounded" experience in terms of ambience and style. Both are incredible. If you go to Battebecco any risotto that they have on the menu will be exemplery, the equal of anything in the entire country. They make it correctly. If I had to choose between these two (and I have in the past) because of the chef/owner I would go to Bitone. It is truly a special experience.
There is also a superb wine shop (enoteca) just down from the Baglioni. The prices are among the lowest in Italy and the selection is excellent. I found '97 Solaia and Massetto there six months ago along with Avignonesi Vin Santo. All three of these are difficult to find anywhere in Italy.
I should also add that sixty miles north of Bologna is Dal Pescatore which is Italy's best restaurant. Near Mantova it has three Michelin stars and was featured in an article by John Mariani entitled "the best restaurant in the world."
It is only 45 minutes away.
Overall Bologna is one of Italy's great cities for food. I envy you for your meals there. Enjoy!
Bologna is actually an incredible bargain considering the quality of the food. For comparison a similar one starred restaurant in Milan or Rome is perhaps 25% more expensive. Bitone is a bit more expensive than Battebecco but it is still reasonable.
Wine at both are relative bargains. Castella di Ama Chianti was 35,000 lira while a '97 Solaia at Bitone was 150,000 lira. (Da Fiore in Venice was 220,000 for this while Taverna del Branzino in Florence was 190,000. All had it in stock last January.
For a good Chianti like Ama and two first courses or pasta or risotto for two (which you MUST have at Battebecco), two seconds and desserts I would guess that you could expect US $80 to $90 at Battebecco and $100 to $120 at Bitone.
Dal Pescatore near Mantova about 50 miles north and considered by some to be the best restaurant in Italy (three Michelin Stars) is 180 to 200,000 lira prix fixe with a larger markup on wine. With the tasting menu and a similar wine (although here there is a temptation to order, say, a super Tuscan) you're probably in the $250 to $300 range depending on the wine. It IS worth the journey.
Bologna is one of my favorite cities in Italy, largely undiscovered by many tourists. There that is a great plus however. I should also note that clothing here is somewhat less expensive than Milan or Rome. The exact same Zegna suit that is two million lira in Rome is probably 1.6 here. Testoni shoes (which are made in Bologna) and sell for US $600 and up a pair on 5th Avenue in New York, sell for 600,000 lira in Milan and 490,000 lira In Bologna. That's about US $235 for the same pair that's US $600 in New York. I've found the same to be true for gold, wine, etc. Enjoy.
Personally, I avoid starred michelin restaurants in Italy. They are generally overpriced, "international" style restaurants that one could encounter in NYC. While often excellent foodwise, they lack the unique quality of trattoria's that make dining in Italy so special.
Diana has great food as well as Trattoria Leonida. Both are in Michelin guide and center of town.
In particular all of my suggestions are oustanding. Battebecco is very similar to what you might call a tratorria except that its food is truly exceptional and honestly representative of the area. Bitone is a wonderful experience that considering the atmosphere, food and enthusiasm of its chef/owner is really a value. It is also is authoritatively representative. Neither is what you might call "international."
Neither of these is half of what a good Italian in New York would cost. For myself to go to Bologna and not have the best-at a reasonable price-is a true loss. If you are into wine and enjoy a really good bottle the restaurant cost in both of these is less than a discount store's price in the U. S. And both have incredible wine lists with most bottles not found in the U. S. or elsewhere outside of Italy.
As for Dal Pescatore it is worth absolutely every penny. She grows her own herbs including saffron (!), makes her own butter, raises her own chickens (there are chicken feathers in the parking lot!), uses 40 year gold label balsamic vineger produced nearby-virtually every ingredient in every dish is grown/raised by her. There is absolutely nothing international about this three star. It is unique and an absolute treasure easily worth crossing an ocean just to experience. Neither San Domenico or Babbo in New York or Zafferano in London (which are all excellent restaurants in their own right) can even begin to approach Dal Pescatore. To be able to experience this level of such simple but exquisite food so expertly and imaginatively prepared is a treasure. Have you ever had four year old reggiano parmigiana or 40 year old balsamic or saffron of this depth of flavor and aroma?
I have eaten at over 40 Michelin starred restaurants and this and El Raco de con Fabes outside of Barcelona are for a food obsessed person such as myself a life's reward to experience. They make up for the kind of starred restaurant you speak of. Yes, they do exist in Italy such as the overpriced, stuffy Il Desco in Verona, perhaps enoteca in Florence and several others in Milan and Rome. But da Fiore in Venice and several mentioned in a previous post about white truffles in Alba are extraordinary. You won't have this kind of an experience if you prejudge and don't go.
Will post more if I am able, but for now:
Trattoria di Gianni (off main Piazza in Bologna): great trattoria, very reasonable, doesnt approach michelin star status, but excellent food if you are looking for a non-blowout dinner or an exceptionally good lunch. Need reservations.
Locanda Solarola (Castel di San Pietro, about 25 KM south-west along A14): 2 michelin stars, converted barn-restaurant, with excellent set menus and a reasonably priced wine list. Two of us had five courses with a bottle of wine each and grappa for about 150 pounds, not bad for two michelin stars.
Cane (Dozza, about five km from Castel di San Pietro): kind of cheesy looking restaurant with phenomenal, very reasonable food in a beautiful little fortress town on hills overlooking the farm land for miles around. A real high point. In addition, the Castel in Dozza houses the regional wine center for Emila-Romaga with a great range of wines, again at very good prices. Your only regret will be how many you have to leave behind.
As I said, I will try to write again with more detail. There is some great food in Bologna, and in particular a great range of grappa is served at many of the restaurants, consistently more than I have seen in other areas of Italy, which is strange because I dont think they produce much grappa in Emilia-Romagna.