The Longueuil parking lot is outside, and in winter and because of car theft and such, you might want a covered lot instead.
One of the easiest to get to happens to be one of the cheapest: under the Grande bibliothèque (main library) on the eastern edge of downtown -- so coming in from the East you'd take the Jacques Cartier bridge, stay in the right hand lane as the road curves around 180, take the first right onto de Maisonneuve, continue for oh, 18 blocks or so, turn right on Avenue Savoie which is the little alley after Berri and the parking lot entrance is halfway down the block on your right.
I understand big cities making someone nervous, and Montréal drivers are quick and assertive (and good, actually). But surely he can handle a bridge and a sharp curve and around 2 kms of driving in the city?
To get back out of the city, you turn right onto Avenue Savoie from the parking lot exit, then right on Ontario, then right on Papineau, and then left lane which merges onto the Jacques Cartier bridge.