Recreational linguist Dan Tilque researched this topic, which was published in Word Ways in 2001. He utilized the US Geologic Survey's Geographic Names Information Service to discover that while Springfield is commonly thought of as the most prolific place name, the place name of Riverside can be found in all but four states (it does not exist in Hawaii, Alaska, Louisiana, and Oklahoma).
The runner up was Centerville in 45 states, followed by Fairview (43 states), Franklin (42), Midway (40), Fairfield (39), Pleasant Valley (39), Troy (39), Liberty (38), and Union (38). Springfield isn't even in the top ten (only 35 states have a Springfield).
Tilque concludes that there's no toponym in all fifty states.
While Wikipedia provides a list claiming to include the most popular incorporated places, their list also includes Census Designated Places, which are not incorporated cities. Nonetheless, their list is interesting and shows the toponym of Greenville as a Census Defined Place or incorporated city in 34 different states.
The runner-up for most popular place name on the Wikipedia list is Franklin (26 states), followed by Clinton (21), Madison (20), Clayton (19), and Marion and Salem (18). They claim that Springfield is found in 17 states.
Thus, it would definitely appear that there simply is not a place name to be found in each of the fifty United States but Riverside is the most popular toponym across the fifty states.