The United States has been lucky. I doubt there is anyone alive today that has seen the CONTINENTAL United States as a battle zone (1865).
The last time for Alaska is 1942 (Battle of Midway but there was pretty much nothing there). Hawaii was in the theater of operations for the entirety of American WWII.
Yee-
A couple of corrctions. The attack on Pearl Harbor (Dec 7, 1941) certainly counts as a battle, though a rather one sided on. And there was pretty much quite a lot there.
In Alaska, the Japanese
attacked Dutch Harbor, Alaska on 3–4 June 1942. The
Battle of Attu took place from 11–30 May 1943, and was a serious land battle in every sense if the word, with 549 US killed and over a thousand wounded. The Japanese garrison was almost entirely wiped out, with about 2850 killed, and 29 who were taken alive.
While it probably doesn't quite count as a full on "battle", in the contiguous 48 US states, in June, 1942 a
Japanese submarine shelled Fort Stevens, Oregon. This is believed to be the only time in WW II that a military installation in the lower 48 was directly attacked. For a summary of other WW II engagements in and around North America, see
Wikipedia's "American Theater (World War II)". In particular note the many naval engagements with U-Boats off the E Coast.
NOTE: I have always disliked the term "Continental United States". The last time I checked, Alaska was part of the same continent (North America) as the 48 "contiguous" states.