Best place to go in Black Forest

Staying in Freiburg would be my advice, though it isn't necessarily peaceful and quiet. It's a beautiful city and, like most of Germany, has great public transportation.

I am considering that area but I was concerned that it would be more like staying in a big city. Any suggestions for a sweet spot to stay?

if you base in a handsome old-world town like Gengenbach, which shares the scenic Black Forest Railway line with Triberg, you'll find it easy to reach Triberg and other popular destinations, like the Vogtsbauernhof, half-timbered Schiltach, and Haslach. It's definitely a sweet spot to base yourself and explore the region.

https://www.black-forest-travel.com/gengenbach/

Triberg and Villingen are popular also and within an hour of Gengenbach.

Another vote for Gengenbach for all the reasons RJean mentions. It's a good base for visiting the Black Forest. it also participates in the Konus Card, which gives you free access to the regional trains in the area. Great town square (triangle, actually) for watching the world go by as you eat gelato from the nearby Italian restaurant.

For your list:
Relaxation -- check
Beer gardens -- check
Easy hiking -- depends on how easy you want
Great Food -- I liked what I ate there (but I'm pretty easy to please) -- reasonable # of restaurants
Peace and Quiet -- check

can I pile in for Gengenbach?

Proceed Nigel

Gengenbach, followed closely by Staufen (I've not visited the northeastern part of the Black Forest, Bad Wildbad, Horb, etc))
Gengenbach has river and hilly walks close by, the vineyards around Durbach are attractive. Baden-Baden a short train ride away, Freiburg can be visited by free train (short route or a longer, more scenic route via Donaueschingen). https://www.stadt-gengenbach.de/index.php?id=4

Staufen is a little gem, a short train ride away from Freiburg, a reasonable train ride away (with stops) from Gengenbach. Lakes Titsee and Schluchsee can be reached easily enough, the latter having a nice hike around it. There is a pleasant, easy walk from Staufen to Bad Krozingen by the side of a creek. There is a nice ruin above Staufen, with more hiking beyond it. https://www.staufen.de/,Lde/299877.html

As one who always drives, I would not normally consider Freiburg as a base because of its size, which may also affect your decision. But as you are using public transport, Freiburg is not such a bad idea. You can easily reach Gengenbach and Staufen from there, it has a nice old town and there is some nice hiking to be had on the hiking paths on the east part of the city past the obervaton tower.

The Black Forest is not Swiss Alps stunning but it is pretty as a picture in parts and has its charms. I once read a laughable opinion that it was not worth visiting if you had already visited the state of Michigan.

Jumping on this thread( hope thats OK ,Debbie) would

Gengenbach be easily accessible from Basel by public transport

Thank you all for your suggestions. They have given me a lot of options and wonderful insight into this beautiful area of Germany.

My wife and I enjoyed Freiburg - especially the daily market in the Altstadt where we packed a lunch from different vendors per RS advice. We stayed at the Park Hotel Post just two blocks from the train station (cozy and artsy) and made great use of our two days there by booking a personalized tour with Simone Brixel who RS recommends. Though we prefer to explore on our own most times, we found that her extensive knowledge of the Black Forest gave us an experience we could not have replicated on our own no matter how much research and planning we might have done.