Generally it would be nice to show timezone offsets anywhere times are shown on AlertSite, as it is incredibly hard to know what timezone monitors and alerts are relative to. Especially if you are not an admin.
But specifically, it would be nice if the blackout periods for an alert showed the timezone they are set for. We had an issue where blackouts were set not realizing which timezone they would apply to since the account was set for a different one. Then the account timezone was changed, and because of the lack of an offset display we assumed the blackout period would update to reflect the new timezone offset, assuming that the display was relative. The blackout display did not change which led to wondering what timezone they actually were configured for. It would be nice to be able to see this explicitly in the UI and not have to guess.