it is quite possible to play without a map...
it is likely to be easier to have a map both for the players and GM, but it can be done with just notes, but then its more likely to have things "drift" around.
one thing that can be done, is grab a map of a town or a city a long way away from where you are, and replace things with setting correct examples.
IE a junkyard today (for cars busses, trains, etc. ) in battletech/MechWarrior will have all of the above, plus junkyards for tanks, and mechs.
a pawn shop or gun store is likely to be more or less the same but with more "battletech" gear in it.