There are a number of approaches to the problem of varying difficulty/complexity, pros/cons.
The easiest is a fixed offset, a one-time configured item during the initial installation. Let’s say the server time is EST. An offset of +3 would shift all times to PST. This would apply to all web sites. Everyone would see the data relative to that timezone. (Or we could convert all times to UTC and just specify a timezone offset relative to that.)
Another scenario is a fixed offset per web site. This might be a middle-ground solution.
The most difficult would be user-configurable timezone settings per user. This is complicated by the storage of timestamps in server time (vs UTC) and how archiving currently works. We could leave archiving alone (i.e., by server time). Or we could archive by user timezone – unfortunately, this has the negative consequence of increasing the database size significantly.
We would also need to consider how to handle DST and re-archiving when someone changes the timezone settings.