If you have 2-3 hours to spend in Greenock, you should consider visiting the McLean Museum and Art Gallery, which houses a collection of local history, archaeology, and art. It will take you approximately 1-1.5 hours to explore the museum thoroughly.
Alternatively, you can take a walk along the Esplanade, which offers stunning views of the Clyde Estuary. It will take you about an hour to leisurely stroll along the promenade.
If you're a fan of historic buildings, consider visiting the Custom House, which was built in 1818 and has now been repurposed as a cultural center. You can take a tour of the building, and it will take you approximately an hour.
Finally, the Victoria Tower on Union Street offers panoramic views of Greenock and the surrounding area. Climbing to the top takes about half an hour, and the view is well worth the effort.