I have watched the DVD again, and took notes as to where the Martians were concentrated prior to the nuclear strike: The scene starts at 56:10 on the DVD.
North America: Canada from Central Sask. to the U.S. border (Northern Minnesota), a major concentration in Northern Alberta and Sask., and from Montreal east through the Maritime Provinces, but not PEI or Nova Scotia.
U.S: Seattle down towards Idaho and Northern Nevada, San Francisco Bay Area-Sacramento, L.A. area. No sign of landings near NY (the report of landings on Long Island mentioned pre-battle could be a false alarm).
Mexico: Mexico City and vicinity.
No Martians in Central America or on any of the Caribbean islands.
South America: A small concentration in either Ecuador or Peru (even pausing and zooming made it hard to tell), a large concentration from Santiago east to Buenos Aires and on to Rio. Also a large group in Brazil's NE tip going to the NW along the coastline.
Europe: UK: London south to Dover. France: Bordeaux NE to Paris. Portugal from Lisbon east through Spain (Madrid) to the Med Coast. Norway: Western Norway (Stavenger area, looks like, not Oslo). Sweden: area around Stockholm. Italy: Po River through Rome south to Naples. Yugoslavia: Most of the country. A small group in European Turkey. In Eastern Europe, Hungary all the way through Romania into Bulgaria. Narration mentions Finland, but the map room scene has nothing in the country. The USSR: A large concentration from the White Sea (Archangel) to the southeast. One large concentration in European Russia possibly from Leningrad down to Moscow (hard to tell, even with pausing the DVD and zooming) Several major concentrations in Central Asia (one from the Iranian border NE through Astrakhan) and in the Soviet Far East.
Africa: A large grouping along the Morocco-Algerian border due south-those two were French at the time, along with what was French West Africa. A pair of large groups from Cairo down to the SW towards Chad. South Africa has the central part of the country occupied from Pretoria-Johannesburg down to Durban and to the west. Also in Namibia. Madagascar is cut in two through the middle of the island.
Asia: India from New Delhi south almost to the tip. Most of Burma is also occupied, along with some points in what was French Indochina. (makes one wonder how the Vietminh and the French handled this...) Scattered landings in the Philippines, Borneo, and Northern New Guinea. Japan has landings in three of the four Home Islands (Shikoku excepted). China has a large infestation starting at the Yalu River and going to the NW through most of Manchuria. A second major grouping starts at Beijing and goes down to Shanghai, then west along the Yangtze. A third grouping seems to be S of the Mongolia-PRC border. No Martians in the Malay Peninsula, Korea, Taiwan, Okinawa, Asian Turkey and the rest of the Middle East.
Australia: Most of the interior...Darwin South to near the South Coast, along parts of it, then east to Sydney, and north, with the Cape York Peninsula cut off. The map does not show NZ.