A good question.
A local answer.

Use the current Transport Canberra planner for your arrival time and luggage. Bus routes and payment methods can change.

Check the walking distance between the Gallery and Library and from each stop to the entrance. Leave time for security, exhibitions and a meal.

Use the current local transport planner from the railway station, including the walk to the bus stop and any transfer. Route numbers from an old post may be obsolete.

Group nearby sights into one area per day, then compare current bus travel times with the cost of parking at each stop. Google estimates may miss weekend frequency.

Enter the archive and your starting address in the current transport planner. Route numbers and timetables can change, so use today's service rather than an old forum answer.

Build the trip from the current regional rail and coach timetable for the actual weekday. Services may be infrequent, and a connection that once existed may no longer run.

Check the current bus planner for the day and arrival time, including the walk from the final stop. A taxi or rideshare may be simpler with luggage.

Ask a licensed taxi or transfer provider in advance whether it can supply the correct restraint and confirm that request in writing. A standard car arriving without one may not solve the trip.

Plan each cluster of sights together and check its current car-park map. Availability and time limits vary by institution and event.

Compare current door-to-door schedules and total fares for your flight date. A bus to the airport can be simpler than rail plus a Sydney transfer, but timetables vary.

The accommodation may accept bags before check-in even if the room is not ready. Confirm that first; it could save a separate storage fee.

Confirm the event's current launch site and start time first; balloon flights depend on weather and may move or cancel. Check the organiser's transport advice for that morning.