So in Pathfinder every corner of the inner sea has a Pathfinder lodge with a venture captain holding the fort, and it's a handy story hook and player resource.
So is it the same in Starfinder? Are there field offices other than the lorespire complex?. I've mostly been running Dead Suns and just read a couple of the society scenarios andI haven't seen any mentioned.
Depends a bit on how much you want the Starfinder Society season arc(s) to influence your universe.
The reason you don't see much about it from the Society scenarios is that they lost most of their personel assets to an event called the Scourged Stars. It's the meta-reason for all the new player agents, they are training new agents as fast as they can.
Before that event they had extensive holdings and personel. You can pretty much drop them wherever you feel necesary.
I imagine there are a lot of understaffed and vacated lodges spread out across the Pact Worlds and the galaxy. There are also a lot of new, inexperienced recruits. The lack of people and resources allows for a lot of plot hooks.
The Scoured Stars Incident is a huge influence in my game. The only more impactful event is the Gap. I'm playing the Starfinder Society as desperate to rebuild itself and hold onto its remaining resources, while the other organizations in the Pact Worlds look to take advantage of the Starfinder Society's situation.
There has been mention of lodges, both in the pact worlds and other locations. Even mention that there was more lodges in the past but past leadership decided to abandon some (many?) in the vast and focus resources on lodges closer to the pact worlds. That was even before the current period which suffers from reduced manpower now.