Our first royal visit was by Prince Alfred, Duke of Edinburgh. He was Queen Victoria's second son, unlikely to succeed her, and carved a distinguished naval career. In command of HMS 'Galatea', he made three goodwill voyages to the far-flung colonies, and had a great reception (including surviving an assassination attempt in Sydney). On the first, he arrived in Australia in 1867, and stayed for 6 months.
There were no electric, cable (or horse?) trams, but VR ran a royal train to Bendigo, hauled by 2-4-0 loco 50 (later classed B), dating from 1862, and fitted with a cab. Such luxury; the pioneering days had indeed been left behind. Away from suburban Melbourne, VR reached Ballarat via Geelong, and had reached Echuca. The beautifully-constructed railway, to British standards, must have been the VFT/shinkansen/TGV of its day, and the pride of the colony.

I doubt that subsequent royal visitors travelled by street tram, but trams must have been essential for moving the assembling onlooker crowds.
IIRC Prince Charles and Lady Diana travelled on one of the tourist-tram lines during their 1980s visit, but that is in a more-recent era.

Hitler didn't want to come to Australia:
The Ryanair option: www.youtube.com/watch?v=4Zs0IRiJN4A
but did get here when Mussolini was unavailable to make trains run on time.
VLine www.youtube.com/user/VlineFuhrer
Geelong line www.youtube.com/user/VlineFuhrer#p/a/u/1/f5A2yhy1FnA

Roderick B Smith
Rail News Victoria Editor

"Bill Johnson" <pincush@...> wrote:
Conan Doyle...visited Melb around 1929 and was impressed by the cable trams..

From: mike_johnson_melbourne
Monday, November 01, 2010 12:50 PM
the distinguished London journalist George Augustus Sala dubbed our city "Marvellous Melbourne" in 1885
Agatha Christie certainly visited Australia....Mark Twain (Samuel Clemens) who attended the 1895 Melbourne Cup. He must have ridden on a cable tram during his stay.