There are a few timelines I'd like to live in: my timeline of Bazaar, Gernsback from GURPS Infinite Worlds, a Draka timeline (providing I can be a Draka), a timeline where technology is far in advance of OTL (something similar to The Culture from Iain Banks' novels), or the world in the novel News from Nowhere. I'd also like to live in the Anglo-Dutch Empire, but in the 1920s or 1930s, not in the present day. It would be somewhat like OTLs 1920s/30s, but better, because people would be less uptight about things and there would be no major wars or depressions to spoil things.
As for my role, I think either some kind of teacher/scholar, a businessman, an aristocrat or a successful comic writer (maybe I could be the Draka equivalent of P G Wodehouse?). As long as I'm wealthy enough to be able to travel , I'll be happy.