In Australia, the approach has varied state by state.
Three of the six mainland states - Queensland, South Australia and Western Australia - closed off their borders to non-local residents, and still have, though the first two are reopening on 10 and 20 July respectively.
So did the island state of Tasmania and the small in population (c.200000) Northern Territory. Tassie like WA has yet to announce a reopening date, so mainlanders cannot visit.
These closed states have typically enforced 14 day quarantine for people returning.
The two largest states, population wise, of NSW and Victoria did not close borders.
Melbourne to Sydney has had the XPT twice daily (like a British HST, but max speed 160kmh and better aircon) trains resume. They had been not operating between Albury and Melbourne between 20 February and about 4 June due to the Wallan Loop XPT derailment that was no fault of the track, but severe speed restrictions were imposed. The operator (NSW government) of the trains is enforcing social distancing on board (reserved seats only, strangers not booked together) but as with all Oz railways and public transport, no need to wear a mask.
The 'Indian Pacific' and 'The Ghan' transcontinental trains were to recommence on 1 July 2020 but borders won't be open by then.
V/Line, NSWTrainLink and Queensland Rail didn't cancel many trips, rural or interurban.
Bear in mind of 25 million, only 102 have died with fewer than 8000 cases, so different (arguably 'safer') than USA, Europe, UK or many other places in the world.
Cafes in the various states are now allowed to have one person per four square metres while in some places like South Australia, some pubs have reopened. Hotels (for accommodation) are mostly open again, while the ski season in NSW and Victoria (Thredbo and Mt Buller/Hotham and the like) opens between 12 and 22 June 2020.
I don't know any heritage railways that have reopened. The former Victorian Railways branch line (Victorian Goldfields Railway, linking the historic towns of Castlemaine and Maldon, Vic) is closed, as is world famous Puffing Billy in Melbourne's Dandenong Ranges at Belgrave.
Some rail tour operators like St James Rail (based in Sydney) are starting to operate local trips, but international travel is impossible as Australian citizens are not allowed to depart, and foreigners not allowed in.
Patronage on our metropolitan rail, tram and bus networks is way down but is gradually recovering, and will improve further once offices reopen to more.
Melbourne to Sydney used to be easily in the top five domestic air routes with up to 75 flights each way a day but this is currently down to about three to six, although by the end of July may be up to about 20 each way, fewer on Saturdays. The second airline Virgin Australia is in administration with more than A$7 billion in debt, and may in the end be liquidated.