How can I determine the distance between Olympus Mons and the closest point of Valles Marineris?
What tools are available to the general public for these kinds of queries?
One of those tools is this calculator on the NASA website.
Let's see what it gives us here:
According to the calculator, the distance is 2387.8 km.
(Note that in order for the lines on the map to match, you need to enter Point 1 as 18.65, -226.2 and Point 2 as -7, 102.2, so the longitudes are the negatives of what is mentioned in the instructions):
Depending on which point you choose in the Noctis Labyrinthus, the distance may be a bit less or more.
There's some ambiguity about whether Noctis Labyrinthus is part of Valles Marineris.
According to Wikipedia it is part of the Valles Marineris system, but it also says that Noctis Labyrinthus is a region between Valles Marineris and the Tharsis upland.
Anyway, Mars Trek is an excellent tool to determine distances and elevations on Mars.
Press the "Skip Tutorial" button and zoom in once, and you already see Olympus Mons at the left with the other three shield volcanoes.
At the right corner below you see the latitude and longitude values and with that you can find the western edge of Valles Marineris.
Then press on the menu button in the upper right corner and choose the "Calculate Elevation Profile".
Then select "Line" and press down on Olympus Mons and let go on the western edge of Valles Marineris.
Then the distance is shown and if you press the "Submit" button you get the elevation profile from Olympus Mons to Valles Marineris.
If you choose the most north-western edge of the canyon of Valles Marineris the distance will be about 2888 km.