Order of the light DRAFT!

Much of the dyson sphere is uninhabited, but there are two main areas of note that aren't maintenance corridors and access tunnels. 
      

from this truly terrible drawing I did as a teenager, you can see the general vibe of the exterior. 
Around the equator of the Dyson sphere are many different port entry areas, some modified to house much larger ships, though, probably not the size shown in the concept art. wide bays with renovated docking equipment that was brought in to be able to adapt to different ships than those the builders left behind, (which perhaps they left a considerable defense force.) 
the cholor scheme that I imagine would be an almost gemstone like blue glassy surface making up floors and parts of walls, with gold-plated metal creating structure and accent. the area around the hangars are generally reserved for supplies, training rooms, and  bunker like structures that appear to be particularily reinforced. 
the only way that it makes sense for transport on different parts of a dyson sphere would be either a crazy fast sublight shuttle or train service, (which is a fun picture) but based on the smaller scale of the organization as is being supposed for this version of the story, transporter beam me up scotty style transportation is a much more likely candidate for moving small groups of people vast distances quickly. 
That brings me to the city at one of the poles of the planet. shoot that doesn't make sense on an astronomy/physics sense
there is going to be some crazy whoah magnetic interference at the poles because a star's magnetic feild is... a tad bit strong. so instead somewhere along the equator too is a big city where their 100% solar powered floor heating is contrasted by a big glassish dome and a view into the ever night stars 24-7. This city would become the main headquarters of the order, where they have temporary lodging or travellers in need, and use the old government buildings of whoever lived there as the meeting and strategy rooms of the order. lots of labratories with old equipment and possibly some old unfinished technology that they are working to complete so that they can get more stable gateways between universes, and/or maybe get ways to jump to universes that are not adjacent to the launch point of the individual. 
think really pretty golden city under the stars, that at the same time is abandoned and somewhat barren.... oohhh
maybe I should write about when the first people got there and come upon this dyson sphere that is the home of a dead civilization who almost figured out how to leave their universe, and if new people decide to make their home there the mass graves and/or monuments to be constructed in the honor of those who built it. hmmmmth

I have to go back to work but this is what you get.

Type

Secret, Military