A related question to your question would be, What was Bacon's idealism like? I would first answer this question. Then, I will discuss the essay, "Of Great Places," in the light of his idealism -- as I understand it.
Francis Bacon's Essays were published in 1597. He described his essays as "counsels..civil and moral." Apparently, these essays were written for ambitious university educated young men who aspired to "great places," i.e., --in our parlance --high ranking officers in administration.
Bacon himself was a very high ranking officer; served as both Attorney General and Lord Chancellor in Queen Elizabeth's court. (Lord Chancellor used to be the old name for prime minister. The difference was that in those days the monarch chose her own prime minister whereas in Parliament the elected officials choose a leader to serve as prime minister). Add to that the fact that Bacon is also regarded as a pioneer of modern science as we know it, arguing for the importance of accurate observation of natural processes, faithful recording of the observations and making logical conclusions from the observation -- we have a formidable intellect and a philosopher.
The critical opinion of Bacon used to be that he was a Machiavellian; meaning, Bacon was like Machiavelli, the Italian statesman of the later middle ages given to perhaps a bit too much practical wisdom! But, in my opinion, that sort of critical estimate was based on the written histories of England. I am willing to concede that Bacon privileged pragmatism to abstract idealism; what I have more trouble with is the moralistic pronouncement on the man.
Bacon's idealism may be deduced from his intellectual productions. A contemporary of Galleleo and Descartes, Bacon was a severe critic of the intellectual milieu that pervaded his times (Descartes, Galleleo were exceptions -- the latter was, in fact, a victim of the church because of his scientific knowledge). Bacon discarded old science of the alchemists and kept on pushing relentlessly to the scientific method that I have briefly outlined above.
In his personal-professional life, he worked tirelessly and rose from position to position. Then, there was the fall. He was convicted of corruption and imprisoned and forcibly retired from public life, not unlike what happens, time and again, in the US today.
It was during this period of forced retirement that Bacon produced most of his written work. In the essay under discussion, "Of Great Places," Bacon writes which, in hindsight, is no small irony: "Nay, retire, men cannot when they would, neither will they, when it were reason; but are impatient of privateness."
"Of Great Places" distills Bacon's idealism about personal and professional idealism. Brimming with terse, literary sentences, typically Baconian, this essay attracts readers' attention through stylized brevity. The very first sentence of the essay --" Men in great places are thrice servants" -- would be a very good example. He had a sense of balance. His sentences were cryptic and elegant: "It is a strange desire, to seek power and to lose liberty: or to seek power over others, and to lose power over a man’s self. "
I think what Bacon tries to convey with this style, and with his subject matter, is that triumphing in public life is in itself a "science." It is not a matter of hot-eyed humanistic idealism. Rising to high places is laborious, he says. But it is important to rise to these places in order to do public good.