Florence City Center good areas/bad areas?

Well, you are lucky. There are no bad neighborhoods in the historical city center.
Unlike the US, in Europe the bad parts are in some of the suburbs and the areas in the outskirts, while the inner cities are all good parts.
Florence actually doesn’t have too many bad parts even outside of the city center. The less desirable areas however tend to be on the west side of the city, far from the center (Scandicci, Isolotto, Le Piagge, Peretola, Brozzi,...).
In the city center everywhere is good. The area between Piazza della Signoria and the Duomo is the busiest (with tourists). The Oltrarno (south of the river Arno) is a bit quieter.

As Roberto stated, there are no "bad" areas in central Florence. We LOVED the city and hope you do as well.

wonderful to hear. this is the information I expected after researching online, but wanted to ask those who have actually traveled there as tourists.

thanks so much!

Here's one take on Florence neighborhoods, from EuroCheapo: https://www.eurocheapo.com/florence/hoods/

What would one find if one decided to stay in the so called bad parts? Are the pickpockets as prevalent in those areas as in the historic center where most tourists stay?

There are a few alleys that are better avoided; the back of mercato centrale (via Panicale, via Chiara) and via Palazzolo/via dell'Albero/via del Porcellana near the station. They are not so dangerous you can't walk, just unpleasant. The gardens on the back of Fortezza da Basso are the new drug outlet area and are definitely to be avoided.

Thanks for the additional information!!

I also would say that if you're sensitive to street noise , not to stay within the area around the Duomo.
There are a lot of students in Florence, and they make a heck of a noise late into the night; and with the stone narrow streets, the noise echoes and you might not get a good sleep.
Then after they've all gone to bed, the street cleaners and delivery carts and garbage collectors start up quite early.
I would stay across the river in the Oltrarno area, and in a small street with no shops or bars nearby.
You can look on Street View and have a walk around to look at your intended neighbourhood.
Florence is amazing, and has so much to delight you!

Unlike the US, in Europe the bad parts are in some of the suburbs and the areas in the outskirts, while the inner cities are all good parts.

This throws first-time American visitors to Europe for a loop, the outer edges of cities are the rough areas (public housing, indigent, manufacturing) whereas the closer you get towards the center of town the more affluent or, appealing the areas become. All cities have their dark spots in Florence you'll very likely not have any issues.

Florence isn't that big of a city, and you'll very likely not run into any 'bad areas' unless you're seeking trouble.
Find a map, draw a line tracing between:
Santa Maria Novella (Train Station) - Piazza della Liberta - Church of Santa Croce - Piazzale Michelangelo - Pitti Palace - Santa Maria Novella
Roughly within that box, is where you'll likely spent your entire time in Florence and within that is endless accommodation possibilities. Unless you're seeking a top-notch hotel, most places will be nondescript on the outside except for a sign or, plaque. Some accommodations will occupy the same building, one business on the top floor and another on a separate floor. If you're on a main street, you may get the wake-up noise of garbage and delivery trucks doing their rounds in the morning. Most accommodations are above street-level, it helps keep noise to a minimum.

" Most accommodations are above street-level, it helps keep noise to a minimum. "

I respectfully disagree with this sentence.
I've stayed in Florence eight times in different areas of the city; and if your bedroom is at the front on a busy-ish street, the street noise is going to funnel up the narrow street with stone buildings, and be just as loud as if you were at street level.

Last October, I stayed in the Sant' Ambrogio area of Florence. It was perfect, just far enough away from the main central tourist area, but close enough to walk to the Duomo, Santa Croce, or Accademia in 10-15 minutes. I stayed at an Airbnb apartment, but saw a few small hotels nearby. Very quiet in the evening and I felt comfortable walking around in the day and evening as a solo female traveler.