One US city hospital with a misguided notion . . . (3,7)
I believe the answer is:
san antonio
'one us city' is the definition.
'San Antonio' can be an answer for 'city' (San Antonio is an example). I'm not certain of the 'one us' bit.
'hospital with a misguided notion' is the wordplay.
'hospital' becomes 'san' (short for sanatorium).
'with' is an insertion indicator.
'misguided' indicates anagramming the letters (letters guided into the wrong places).
'notion' anagrammed gives 'ntonio'.
'a' going within 'ntonio' is 'antonio'.
'san'+'antonio'='SAN ANTONIO'
Can you help me to learn more?
(Other definitions for san antonio that I've seen before include "Texan mission location" , "Texan city, home to the Alamo" , "city in the New World" .)