(nbigpigeon.us webpage WW II - Japan > South & SW Pacific, updated by RAC 6 Feb 2020.     Not quite complete.
Major US land combat in the South and Southwest Pacific Theaters began in August 1942 with the US Marine Corps invasion of Guadalcanal and ended with the US Army's September 1944 invasion of Morotai 2,300 miles to the northwest.
1942-44 US Path Across the Southwest Pacific
1942-1944 US Path Across the Southwest Pacific
Links to the WW II - South/Southwest Pacific subpages 
The Japanese Invasion of Melanesia - Early 1942
Japanese forces first occupied key points in the Bismarck Archipelago, in the center of the accompanying map. The only substantial resistance was at Rabaul in the Bismarcks. The Japanese then began developing Rabaul into the main Japanese base in the South/Southwest Pacific.

Note the initial Japanese landings in Northeast New Guinea.
Japanese Advances in Melanesia - Early 1942
Japanese Advances in Melanesia - Early 1942
I view WW II US ground operations in the South and Southwest Pacific as consisting of two phases.
Phase 1 - The Eastern New Guinea and Solomons Areas - through March 1944
Until April 1944, ground combat in the South and Southwest Pacific Theaters was confined to the areas shown on the accompanying map, namely:
  • The Solomon Islands (US Marines and Army).
  • Eastern New Guinea (Australian and US Army).
  • Southern New Britain and the Admiralty Islands (US Army and Marines).
During 1942, Allied operations were primarily intended to remove the imminent Japanese threat to Australia. 1943 operations, with the overall name of Operation Cartwheel, were meant to neuter the Japanese base of Rabaul at the north end of New Britain.
The Cartwheel Area
The South and Southwest Pacific Theaters - August 1942 - April 1944
Phase 2 - Western New Guinea - April to September 1944
In early 1944, Marine Corps forces in the South Pacific were withdrawn for use in the Central Pacific campaign, which had begun in November 1943 at Tarawa. 

General Douglas MacArthur's Army forces on New Guinea and his supporting navy fleet were now sufficiently resourced to allow a rapid advance across the north coast of western New Guinea and on to the East Indies island of Morotai in preparation for the pending liberation of the Philippines.
Western New Guinea Area
Western New Guinea Area
​Sources for the WW II - South/Southwest Pacific webpage