How does Earth's thermal radiation into space vary by location and time of day?
The yearly average Top Of Atmosphere (TOA) Outgoing Longwave Radiation (OLR) is around 145–345 W/m², as measured by the AIRS instrument:


Source: Wikimedia Commons contributors, "File:AIRS OLR.png," Wikimedia Commons, the free media repository. 

Now, this is an average that includes both day and night.  How much does it vary?  This depends on the location.  Based on GERB data, a 2007 paper estimates (please pay attention to the thick solid line only):


Source: Comer, Slingo, and Allan (2007)

Even in places with a very large diurnal temperature cycle such as the Sahara, the difference between maximum and minimum is only about 10%.  In oceanic areas it is closer to 2%.  That means that if you take the mean (shown in the top figure) and subtract around 1–5% depending on the region (the drier, the more difference) you get a reasonable estimate of the nighttime outgoing longwave radiation.

If you want a more precise estimate, you can always download satellite data and calculate it yourself.



Full source for second figure: Comer, Slingo, and Allan (2007), Observations of the diurnal cycle of outgoing longwave radiation from the Geostationary Earth Radiation Budget instrument, Geophysical Research Letters, Vol. 34, L02823, doi:10.1029/2006GL028229