Hi Jules,
In 2019 I used that bus to get from place to place on two different days. It is not truly a HOHO bus in that it is not a big tour bus, at least from what I remember. It is a smaller size bus and makes the rounds of tourist sites in Siracusa/Ortygia. and I remember it was cheap and the ticket was valid I think for 24 hours. We caught it on Corso Giacomo Matteotti near the Fontana di Diana, because we were staying in Ortygia. I think the first time we got on we did the full round trip to get a feeling for Siracusa/Ortygia. Then the next day we took it to the Archeology Park. The bus dropped us off across the street from the entrance to the archeological park in the parking lot of Bar Dionisio. I found the Orecchio di Dionisio and quarry area to be interesting. It is hilly and somewhat steep in places, but there are concrete sidewalk pathways from area to area. In my opinion the Greek theater and Roman ampitheater there were not as impressive as the ruins in Agrigento, Segesta and Selinunte, and the theater in Taormina, all of which were spectacular. I personally would prioritize seeing all of those other sites over these ruins in Siracusa if your time is limited or if your knee is bothering you. On the other hand, I found Ortygia to be beautiful. Lots to see and do there. Other than the archeological park I stayed in Ortygia most of my time and particularly enjoyed the outdoor market, the beautiful main piazza and cathedral, the castle, the colorful narrow streets, the views as you walk around the town, particularly along the periphery, and a typical Sicilian puppet show at teatro dei Pupi on Via della Giudecca.