Re: The Actual Day Tim Drake - Red Robin (Cardinal Earth): Tim was just in civilian wear but brought his Red Robin utility belt in he back pack, just in case (never leave home without one, kids). He would have stopped for coffee before going to the museum and arrived mid-morning.
Conner might have been with him and they might have run into Dick and explored the museum together. The had a plan to sneak to the basement facility under the museum, where the Cardinal Earth version of Superman was being secretly held in stasis after being poisoned by kryptonite infused into his blood stream 3 years ago. Tim wanted Conner to see his family.