Bari Italy - Bari Vecchia district

Well, I lived 11 years in Bari as a teen; at the time the old city was an haven of crime and only rarely we ventured there; being a music student, concerts at St. Nicola was the main reasons of our visits. Reclaming the area from crime was a major success and I have walked safely there during my visits in the last decade.
IMHO I would start from Piazza del Ferrarese and adjoining Piazza Mercantile, then wander around. The major sights are the Cathedral and the St. Nicola basilica. This last one is very interesting as it houses the remains of St. Claus, so has become a major centre of pilgrimage from Eastern Christians. It is the only Catholic church where an Orthodox chapel (in the underground) has been allowed and you will see both Catholic and Orthodox clergy - I do not know now, but when I visited before Ukraine war, I noted that almost all the offers in the transparent alms box were in Russian rubles. The faith in the saint bishop is so strong in Eastern countries that when the Pope lent to Russia a piece of the remains for a few months, the average queue for visiting it in Moscow was 4-6 hours.
The Cathedral is more impressive than St. Nicola as a building but has not such a spiritual history. Its main piece of interest is the Exultet roll, moved - I believe - a few days ago to a church museum. It is a medieval paper roll, 16 feet long, illuminated with Easter histories and music. As the deacon sang the Exultet on Easter vigil, he unrolled the paper showing the people the pictures - that are painted reversed in direction to the music.
After the two churches, the main sight is the castle, last rebuilt in 1233, but not really so much interesting inside. Then you just soak up in the atmosphere.

Haven't been to Bari since 2015, but it was a fine place to wander in without a guide then. We followed this advice: "Quartiere delle Orecchiette: from Piazza Federico II di Svevia you'll see the Strada Barone, & from there two little lanes that lead into the old quarter with arches. Walk along Arco Alto and Arco Basso.”  There, you'll see the local handmade pasta drying on tables in the streets (streets where only people and motorbikes go and they are sparkling clean). See the main churches, of course, Cattedrale di San Sabino and Basilica di San Nicola --- one of these was closed mid-day (as even churches tend to be in Puglia) when we were there, but Google says they are open all day. Maybe they are, now. But it's the exterior sculptures on churches that we go to see, anyway.

Eat streetfood, like focaccia Barese --- somehow it's just fun to eat a local specialty in the place it's named for.

I hope you get some more recent experiences of Bari from people here.

Wow... thank you for the detailed and useful information. I am encouraged by your advice. And as Nancy said... there may be others who will add even more tips. I am confident that this senior female can go confidently solo and enjoy exploring Bari Vecchia

It's easy to wander around the old part without a guide, here's what we did one day of our week in Bari:
https://slowtravelitalyspain.blogspot.com/2019/11/puglia-bari-in-april-2.html?m=1

Yes, we wandered Bari Vecchia and Murat without a guide for a couple days last spring. I am trying to remember what guidebook we used, might have been National Geographic, we had a few. We speak some Italian, but I don't think it would be a huge problem if you're English-only.

Bari is wonderful. I hope you enjoy and definitely try the focaccia.

Thank you all for your advice and reassurance. Looking forward to focaccia and orecchiette.