Hi  Vanessa!
Well, there are some neighborhood spots that are good. Some suburban places as well.  
Will you be visiting the city or one of the Suburbs?

A lot of places are "temporarily closed" due to the ongoing pandemic and most of the good places are outside of the downtown area. If you can get up to the far North side Middle East Bakery & Grocery is really good and Cafe Selmarie is a great little place, and closer to the downtown area. Up near Wrigely Field there's Julius Meinl. A bit west of there there's Dinkels Bakery. Not a bakery, but Do-Rite Donuts in the loop are incredible (try the pistachio, they're to die for!).

Damatos 1124 W Grand Ave

Great!  There are 3 French shops in Lincoln Park area. La Fournette, Le Macaron, and Vanille. If you like Macarons and French delights.

Coffee. Dark Matters Coffee, Collectivo

Bakeries. Tous Les Jours in Chinatown is funky

When are you visiting in March?

at the Sugar Goat Bakery.   Stephanie's restaurants are really good, she is also now an Iron Chef on Food Network.

https://www.sugargoatsweets.com/

Down the street a nice cafe is called PRINCI, imagine a trendy Starbucks, but with fresh food along with the Starbucks Reserve Coffee.  

There is also Good Ambler around the corner from these places.  

Of course - STAN's Donuts.  

Toni's Patisserie is good, but temporarily closed due to COVID.