Here is a strange reference to ‘the former Sailor’s Home’ in the 1871 census. Is this just a relocation of the Royal Cornwall Sailor’s Home? Probably, but I’m adding this here for information.
DEATHS
...
At Bank House, Falmouth, on the 24th of August, the infant daughter of John E. Downing Esq.
In the 1871 census
"Part of the Parish of Falmouth lying south and south west of the Town of Falmouth commencing with the house formerly occupied as the Sailors Home and comprising Grove Place, Sailors Home, Arwenack and Bar, the Docks..."
The entries are:
1 Bank, unoccupied
2 Bank, William H Toms and family
3 Bank, Sailors Home, John Littlejohn head, his family, (10 boarders, all seamen)
4 Bank John E Downing [Bank House]
then
5 Groves Place
then 4,3 2,1 Groves Place
then Arwenack House, Manor House, Bar, Bar Terrace,
The establishment at 3 Bank is the Royal Cornwall Sailors Home opened in the 1850s.
13 November 1858: Lake's Falmouth Packet and Cornwall Advertiser
Royal Cornwall Sailors' Home – Mr Littlejohns of Plymouth, has been elected as the successor of Mr Pearson, to be provider of the Royal Cornwall Sailors' Home.
On the modern map Arwenack Street runs NW-SE along the waterfront. The section to the south east of the junction with Hulls Lane is Bank Place which then becomes Grove Place. Here is a street view of the buildings in question:
https://maps.app.goo.gl/4yxuMmzrGHWrD1GP9?g_st=icBank House is the large house at the SE end of Bank Place. There is a single building running from Hulls Lane to Bank House, with three main doors. The middle door has a fanlight with the name Admiralty House. Here is a view looking at the entire block: Bank House is the pale-painted house at the end, the rest is presumably numbers 1-3 Bank Place in the 1871 census, with the central, Admiralty House, entrance being the Sailors Home and the nearer door, number 1, being the unoccupied former Sailors Home.