Specifically about the geographic locations users visit from and perhaps peak times.
I'd be really interested to see the most active countries and times.
Analytics data from sources such as Google Analytics (or other 3rd party ones) are not provided to the general public, as far as I am aware anyway. However there are various sources of public information that is visible.
Probably the Quantcast figures for the site are enough for what you're after:
https://www.quantcast.com/ux.stackexchange.com#!geo
The volume of traffic originating from individual countries in a 30 day period. Indexes are calculated by comparing the percentage of a site's traffic from a given country to the pattern of all Internet traffic measured by Quantcast - e.g, an index of 500 indicates that the site gets five times as much of its traffic from the given country than the average Internet site
COUNTRY UNIQUES (COOKIES) UNIQUES % UNIQUES INDEX IMPRESSIONS % IMPRESSIONS INDEX
US 103,167 34.45 59 34.25 82
UK 26,800 8.95 224 11.00 389
India 26,294 8.78 566 7.88 462
Canada 14,291 4.77 160 5.13 180
Australia 9,574 3.20 225 2.96 212
Germany 9,102 3.04 140 3.78 271