What I would do is put main entrances at the ground level on the west side (3rd st E) at 9th ave and 7th ave corners and at 8th Ave to city hall, creating a two-block-long atrium on the first floor west of the c-train ROW. Provide open space, food services, and muster points there. I'd use the top of the ROW as a ramp spanning from the SW corner (3rd St & 9th Ave) entrance to the second level. I'd also build a stairwell and elevator near the NW corner.
I'd also run interior pathways along the east side of the c-train ROW from both NW and SW corners, converging at the east 8th Avenue entrance, where retail and food space could be leased with exterior access to 8th Ave. Reserve a space for a landmark bookstore (think Powell's books in portland or Daunt's in London or that big bookstore in Toronto). Use this opportunity to create Calgary's first revitalized alleyways, converting the N-S alley (already in place, but not depicted in above render) connected to 8th Ave E to well-lit streetfront. Maintain pedestrian and cyclist shortcuts around the building's perimeter. Use the NE corner for auditoriums with extended hours. Midway up the ramp above the ROW, I'd create a public terrace overlooking 8th Ave, above the library entrance.
The second and third floors would maintain an open-air atrium, overlooking the court below, increasingly reserving more space for study carrels, meeting rooms, and offices as you go up. Maintain plenty of window space and light throughout the building. Connect the 2nd and 3rd floors similarly to floors 1+2, with a block-long ramp above the ROW. I might even cram another level into the SE corner, sacrificing ceiling height for floorspace and taking advantage of the variable grade provided by the ramp. I'd also love to see a hanging garden or greenroof installed at least somewhere.
Create a one or two additional towers (in NW and SW corners to create a landmark visible down 9th and 7th aves, with more office and study carrel space above elevators and stairwells. Allow rooftop access for special events.
My design wouldn't build a bridge through City Hall to connect with Stephen Ave, but instead would disperse pedestrian traffic to the C-train, 9th ave, and 8th Ave E. Minimize digging except for a bicycle locker and shower accessible from the south, and loading bay accessible by alleyway.