I think "You visit many inns on the market." is also a correct answer. I am quit sure that "in /on / at the market" are all valid translations for "in foro"
I don't think that "on the market" works here.
"On the market" in English primarily means that something is available for purchase. It's an idiom.
"We plan to put our house on the market in July."
I think this sentence is simply saying that the inns are physically located within a city forum in the Roman empire.
"At the market" and "in the market" are good for simple location, so they could work here, I guess.
But be aware that there are idiomatic meanings in modern English for "at the market" and "in the market" as well.
Thank you for your explanation. I am not a native English speaker and did not know that "on the market" is used only in this sense.