Honolulu is the furthest west state capital but the state of Alaska extends further west due to the Aleutian Islands, (that end only a few miles off the coast of the USSR) . Honolulu is also the furthest south.
The answer is Honolulu ....... It was a question featured in a quiz and I had my doubts, but after checking found it to be correct. Thanks everyone for your replies.
Alaska is actually contains the furthest points east, west and north of the USA. North and west are fairly self explanatory. But the Aleutian Islands (most of which form part of Alaska but some of which are Russian territory) which Eddie mentions actually straddle the 180 degrees longitude line. Those in Alaska are actually either side of the 180 degree line and so the most "westerly" are actually in the eastern hemisphere.