The council is receiving submissions on the proposal until August 8.
In its application, Todd Property says positive effects of the development include providing additional community facilities in the form of a new public walkway, to be formed as a heritage trail, as well as the cafe.
Napier Hospital closed in 1997 after the Government decided to redevelop health services in Hastings as the Hawke's Bay Regional Hospital.
In 2003 the 5ha site was transferred to the Crown Health Financing Agency to manage and sell.
A $20 million sale fell through in 2006 when developer Eyal Aharoni claimed he had been misled about the land's value.
The sale was plagued with problems, as 12 Napier citizens spent more than $10,000 in private funds to challenge the sale in court.
Todd Property Group bought the site - which has spectacular panoramic views, including overlooking the Ahuriri Estuary and the Napier Inner Harbour - in 2011 for an undisclosed sum with almost $9 million of the proceeds going to the DHB and more than $13 million to the Crown Health Financing Agency.
Todd Property Group specialises in planned communities and has residential and lifestyle developments in Auckland and Northland.
The Auckland-based company is part of Wellington-based Todd Corporation, owned and controlled by the wealthy Todd family.