The really good gnocco fritto can be found all over Emilia Romagna, sometimes it's called torta fritta (as in Parma), or a heavier version called crescentine in and around Bologna.
My favorite place for gnocco fritto or torta fritta is Trattoria Corrieri in Parma, incidentally my favorite restaurant in all of Italy. It's what Zuni is to San Francisco. Other places in Parma that I like: Gallo d'Oro, Tabarro, Frank Focaccia, Antica Cereria.
A must visit is Antica Corte Pallavicina to see culatello production from the master Massimo Spigaroli. Massimo catered events for me and colleagues at my grad school in Parma, plus we visited him as a group a few times. There is also a restaurant on site called Al Cavallino Bianco (I think it's 1 Michelin star). ACP is in Polesine Parmense outside of Parma and really only accessible by car.
In Bologna...I'll say this...the best places are small and hard to get a reservation (always recommended). Counter intuitively speaking, it's not a great restaurant town like Modena or Parma. My favorite place is Osteria Bottega (a short walk outside of the city center) for great casual trattoria food w/pristinely sourced ingredients. Other favorites are Trattoria Giampi e Ciccio and Serghei, both in the city center. Great for a drink and a snack is Enoteca Tamburini and Enoteca Italia.
If you have a rental car, I highly recommend a visit to Savigno, a mountain village. I stayed there for 3 days and it was so relaxing and beautiful. Da Amerigo is the place to eat..it's 1 Michelin star plus has a small inn if you want to stay overnight (where I lodged). Also on the main drag is a bar (can't remember the name) with a great little trattoria in back (I can find out the name...the tortellacci al tartufo nero in the link below is from this place). Savigno is really off the beaten path but so worth it...can't wait to return. Btw Savigno is the place for white truffles during truffle season, I just missed it by a week!
In Modena...book Osteria Francescana now...it's been written up a zillion times and Massimo Bottura is all over media these days. Funny enough I used to live a few minutes away from OF but never ate there until a year and a half ago. Memorable.
Because OF gets a ton of hype, other Modena spots get wrongly overlooked. Hit up Hostaria Giusti, a salumeria with 4 tables in the back, in existence since 1600. Great gnocco fritto, salumi and culatello/prosciutto, Lambrusco, pasta, etc. Reserve now if possible. Other must visit is Trattoria Aldina, upstairs across the street from Mercato Albinelli, a landmark covered market that is the best market imo in all of Italy. Inside at a corner of the market is Bar Schiavoni, my favorite place for a great panino in all of Italy. Loll about in Piazza Grande after (my favorite piazza in all of Italy). Lunch only spot worth a visit is Trattoria Ermes...the owner is a real character and it's wildly popular.
Outside of Modena, in Castelvetro, is the heart of Lambrusco country and one of my favorite producers, Opera 02. I'm pals with the guys who run it, Mattia Montanari and Roberto Ballestrazzi. They've got a gorgeous facility...Lambrusco and aceto balsamico production and a small 8 room inn.