In the calendar world (iCal), this is actually supported: a date time without a time zone is a local time only [0].
Sadly, iCalendar is very much tied to using timezones for locations. I expect that if/when Europe finally gets round to abolishing DST, there will be some significant changes to the timezone boundaries, and as a consequence, much hilarious calendaring failure. Dunno if it will affect as many people as the 2007 DST changes in North America, which caused a lot of extra work for people running Microsoft Exchange, because it was designed assuming that timezones never change. And this design error carries over to iCalendar, tho (apart from tz boundary changes) it is better than it was.
And likewise in PostgreSQL you can store timestamp without time zone.
Combine that representation with lat/long gps coordinates and you have what you need for scheduling future events at specific locations regardless of changes in time zone names and offsets.
Whether your calendar software will let you choose how it expresses the timezone and whether the recipient's calendar software will store it that way is another question...