There is also an expresso bar, a creative activities room, and multipurpose rooms that community groups can use for meetings.
A hydrotherapy pool could be included in the facility at a later date. It is not currently in the scope of the project, but the Greater Hornby Residents Association and Hornby Rotary are co-ordinating a community fundraising effort so one can be added.
With the concept design for the Hornby Centre now approved, work can begin on the detailed design.
The procurement plan will go to the council's finance and performance committee on November 5 for final approval.
Construction is due to start by mid-2021 and the facility is expected to open in late 2022.
"The new Hornby Centre will be an important asset for the community and will help plug a gap in our network of community and recreation facilities across the city,'' said Mayor Lianne Dalziel.
"The Hornby community have been pushing for many years for this type of facility and I am delighted that we are a step closer to being able to give it to them. The approval of the concept designs today means that we are on track to get construction under way next year."