I feel like he would have setteld down in megaton, with his sick ass dog.

I think the East coast BoS split up with those who would follow Maxson on the Prydwen and those who would stay in the capital wasteland ans the lone wanderer is the elder of those who remained.

I think they kept on wandering and eventually headed west, with Dogmeat by their side.

^^The people in the Citadel are still loyal to Maxson. There is no indication at all that there was a schism after his rise (in fact, his appointment to elder was actually seen as something the chapter desperately needed after years of ineffective leaders).

While it's unknown exactly what happened to the LW, Afterword (the epilogue to F3 that was included in the game's guide) does establish that wherever he is most of the Capital has no idea. Moira hasn't seen him and it's gotten to the point that, twenty years after the events of F3, the facts surrounding who he was and what he did are getting iffy. Nobody can agree on one version of what happened.

I've always leaned towards the theory that Deacon is the lone wanderer.

Do the brotherhood still have a base at Adams Airforce Base?

After being under the command of Lyons, I can see the lone wanderer not liking Maxson as Elder. They’re probably wandering the capital wasteland or could even be in Appalachia.

^ They do, it's where the Prydwen was built and came from on the journey to the Commonwealth.

Probably chillin in space, partying and livin it up

Sarah faked her death, and they are now happily married on the spaceship shooting down Zetans over Boston

Honestly he would never settle for Maxons new regime, its way too much like the Enclave.