The answer is St. Paul, AK with -19 on 3/14/1971.
Which places have their record lows on April 2 and March 21?
They are in the same region as St Paul Island. Supposedly Shemya Air Force Base had a record low of 2F on April 2 1988. To me, the Shemya reading seems very suspect, but St Paul Island did record a -3F a few days later, so it might be legit. (Cold snaps seem to take a few extra days to reach St Paul Island, though I can't figure out why this is-seems backwards).
The next island to the east of Shemya, Attu, supposedly had a record low of -5F on March 21 1985. St Paul Island recorded a -2F a few days later, so this seems to be legit(?). For Attu, WRCC does show one reading of -15F on November 27 1986, but this does not seem legit. All the other stations in the area were 30-40 degrees warmer, which on a small oceanic island doesn't make sense. St Paul Island was 24F that day, but dropped to 15F a few days later. Maybe an erroneous minus sign got placed in from of the 15 for Attu? Shemya, on the island next to Attu only got down to 27F.
(PS, if you are interested, St Paul Island did record a -26F in January 1919, supposedly at the same location, but the current NOAA site only list records back to 1948).
For that whole region around the southern Bering Sea, April isn't much warmer than the winter months:
Farther north, Cape Romanzof, on the mainland coast of the Bering Sea has a record low on March 15 1966. This one is not suspect. If the Shemya and Attu readings aren't correct, this may be the latest record low outside Hawaii?
A lot of stations on the Bering Sea have their record lows in March and March is colder than January up in the northern latitudes of the Bering Sea.
On the other side of the calendar, the earliest record low I know of in the US outside of Hawaii is Antelope Island, Utah with November 16, 1955, but alas, there is only 20 years of data available so it might not count.
On the record high side, the earliest record high I know of outside Hawaii is Brownsville Texas with 106 on March 27, 1984.
The latest in the year I know of for an all time record high is Eureka California with 87F on October 26 1993. Ironically, Eureka used to hold the earliest record high I know of with 85F on February 17 1930!
Does anyone know of any outside these timelines?
Also, the March 10-11, 1948 cold wave in the High Plains came close to setting all-time record lows in several locations. For example Lamar, CO hit -26 on March 11 which was within striking distance of its all time record low of -30 from the great February 1899 cold wave. Likewise Tribune, KS was -22 on 3/11/1948 while its all time record low is only -25.
The Dodge City KDDC station used to have their record low then too, but it was broken during the cold spell of December 1989. (Dodge City did record lower temperatures at different weather stations before the KDDC station existed though).
For example I view the -14 at Foster Flat (RAWS) on Oct 31, 2002 as the Oregon record low for October, the only state monthly record low that has occurred since -32 at Ukiah on Nov 23, 1985.
October 2002 was an amazing cold spell for the time of year. Several cities in Idaho, Washington, and Oregon recorded their coldest day of the year in October. I don't know of any other times that this has happened in the lower 48. Does anyone else know of any? Several cities recorded their coldest day of the year in the first few days of November 1991, but I don't know of any in October (besides 2002).