Hi there, I'll try my best to answer your question but I'm no expert on either Persian or Ancient History; I'm sure another more knowledgeable user will arrive after to write something more in depth.

For reference, a parasang is an ancient Persian measurement of distance approximately 5.6 kilometres in length. A furlong is an Imperial unit of measurement denoting roughly 201 metres.

The Royal Road's route between Susa and Sardis was described by Herodotus in his work Histories. The following information can be found in a translation of Histories made available as a .pdf by Roman Roads Media; I will link it below if anyone would like to check out the document for themselves, but I digress. Herodotus begins by telling the reader that for much of its length, the road spanned across fairly uninhabited parts of the Achaemenid Empire to reduce the risk of banditry. Starting from Sardis, located in modern Turkey, the road stretches across the historical regions of Lydia and Phrygia (approx. Western half of Turkey).

In Lydia and Phrygia there are twenty stations within a distance Of 94 1/2 parasangs. On leaving Phrygia the Halys has to be crossed; and here are gates through which you must needs pass ere you can traverse the stream.

Herodotus, Histories Book 5, paragraph 52.

If you can imagine, at the end of the stretch, the road (which has been a roughly straight span stretching East) dips in a more South-Easterly direction. Once it passes the mountains on the southern border of modern-day Turkey (the Anti-Taurus Mountain Ranges), the road returns travelling directly East. Herodotus then notes that travelers must cross the Euphrates and Tigris rivers by boat. After, the road turns South-east once again and approximately follows what is now called the Zagros mountain range (modern day Iranian border). The road passes just West of the city of Ecbatana and then continues South-east to Susa.

If then the royal road be measured aright, and the parasang equals, as it does, thirty furlongs, the whole distance from Sardis to the palace of Memnon (as it is called), amounting thus to 450 parasangs, would be 13,500 furlongs. Travelling then at the rate of 150 furlongs a day, one will take exactly ninety days to perform the journey.

Herodotus, Histories Book 5, paragraph 52.

Now, onto the question as to whether or not the Royal Road still exists. In short, no. The road is over 2,500 years old and is a route between two cities that have not been inhabited for centuries (both fell into the hands of invading armies - Sardis to the Timurids and Susa to the Mongols - in the 13th century). However, after the destruction of the Persian Empire, the road was still used by Greeks and Romans alike. Apparently a bridge exists in the city of Diyarbakir in Turkey that was built around the time of Darius I's reign and is located along the supposed route of the Royal Road.

I do apologise if my description of the route is a tad vague; Herodotus's writing isn't exactly clear and uses a number of ancient region names (ie. Cissia, Matienian territory) which I attempted to relate to more modern day features such as mountain ranges. A number of interpretations on the route can be found on google if you need a visual.