Two new bus stops will be installed in Cook Street.
Cllr Millea said: “The aim of the proposals is to balance the needs of pedestrians, traffic and public transport.”
Far fewer vehicles use Castle Street now, as there are better routes to take around the city centre.
Work is expected to start next spring, and take around a year to complete.
The exhibition is open from 10.30am to 6pm tomorrow, 8am to 8pm on Thursday, and 10.30am to 2pm on Friday.
Blue Badge guides will be leading tours of Castle Street at 1pm and 4pm on Wednesday and Thursday, and 11am and 1pm on Friday.
