Rabbi Samson Raphael Hirsch in his Nineteen Letters writes on this pasuk in Jeremiah that "And seek the peace of the city whither I have exiled you, and pray for it to the Lord, for in its peace there will be unto you peace."- means that
"it is our duty to join ourselves as closely as possible to the state
which receives us into its midst, to promote its welfare and not to
consider our well-being as in any way separate from that of the state
to which we belong."
It seems that Rabbi Hirsch is connecting this pasuk to the idea of אור לגויים.
Thus, the meaning of "And seek the welfare of the city to which I have exiled you and pray to the LORD in its behalf" seems to mean that we are meant to "exhibit to mankind a better example of "Israel" than did our ancestors the first time". By doing this, "the entire race will be, hand in hand with us, joined in universal brotherhood through the recognition of G-d, the All-One" (Nineteen Letters, 16:7).
Similary, the following explanation is given by the Haamek Sheilah on Sheiltot d'Rav Achai Gaon, Kidmat HaEmek, Part I 13:1 in the commentary on the pasuk in Isaiah 60:3.
FOR THE SAKE of [Israel’s] righteousness,1 G-d desired to sharpen the glittering sword of Torah and to enlarge the Torah and its splendor. [To ensure] that Israel would be fortified and strengthened by G-d’s Torah, He exiled the Torah’s honor from Babylonia to the province of France. It was a land [whose inhabitants] had not seen the well-arranged light of tradition, [and they therefore] needed to search for the doorway of the palace2 through examination and analysis. They toiled and discovered a new path that [shone] as brilliantly as the sun.
So, it seems to me that the idea of "And seek the peace of the city whither I have exiled you, and pray for it to the Lord" learns us to make sure the "cities" we live in, discover the "new path"- e.g. the path of Torah and that will bring them closer to G-d.