You mean, besides the obvious Baltic substrate?
The first thing we pick up is 'River'. (I'm assuming our observer gets the name as listed in Wikipedia.)
'Rio Grande' is a weird outlier that is best ignored for now. (Of course, another observer with more data from the rest of the Americas would figure it out and peg it as cognate with River.)
North and South are figured out from the Dakotas and Carolinas.
Maybe we could reconstruct 'West', from West Virginia.
Other prefixes: New, San, Saint and Santa. (the last one being a weird outlier).
'City' can be figured out from Oklahoma City, New York City, Salt Lake City and Kansas City.
We can even figure out from Kansas City that it derives from river, not name.
The meaning of 'City' is obviously, 'a place on a body of water' and I can confidently reconstruct 'Salt Lake' for the 'Great Salt Lake' and 'New York River' for the Hudson River.
I don't know what to make of 'New'. I don't know if being aware of 'Mexico' (the country) would help or not, so let's say that name has been lost to history.
City names tend to be prefixed by San with the variants Santa, Saint; Saint is used in one river name.
Santa might be a variant of San, or just a weird outlier, not related at all. But I think it might be an intermediate form. There seems to be a geographical pattern with San, Saint. Saint being found in the East, San in the West, so perhaps the isogloss runs through Santa Fe.
In any case, we don't know what Saint, San, Sant- may mean, so in the meanwhile we'll just say it's an honorific.
We may also notice a common root: Columb-.
Of course, we see the suffix
-on, as found in Yukon, Oregon, Washington, Cimarron, Trenton, Carson City, Jefferson City, Jackson, Boston, Baton Rouge, Houston, Arlington
It seems to have three allomorphs: -ton after s or a nasal, -son after s, r (possibly assimilated in Cimarron).
Other common suffixes: the very common -a and -ia, and the suffix -as, found in Texas, Arkansas and Texas.