The correct English is "The tourists look AT the map." "Look on the map" is incorrect.
You could be looking on the map - that is acceptable. The tourists look on the map (for the exit to take to the park.). Either on or at is fine.
Could you use 'la' instead of 'pe' here. Would it change the meaning?
"Se uită pe hartă " means really reading the map, while "Se uită la hartă " means looking towards the map
"La" is not the correct according to the given sentence in English.
Should be at the map