I clearly remember the Star Hotel being in Nelson Street just a few doors down from the bottom of Prospect Hill and the start of Victoria Street I was living at the Albion Hotel, Church Street - not far away, from 1935 to 1951.
Porters Isle of Man Directory 1889 lists the Star as being in Nelson Street and Prospect Hill (This rear entrance led into a Concert Room, although I don't remember such). The licensee was William H Sherlock.
A full page advert in Porter's directory also boasts -' The Grandest Concert Room and a Commodious Billiard Saloon - with two tables'
Stuart Slack's book - 'Streets of Douglas - Old and New', Published 1996 by The Manx Experience'. ISBN 1 873120 27 3 has on page 108 a partial view of the Star opposite Billy Corrin's Ice Cream Shop.