Baryshnikov's birthplace (4)
I believe the answer is:
riga
'baryshnikov's birthplace' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for riga that I've seen before include "Fix a rig up here for the Latvians" , "European capital" , "Baltic port" , "A rig in Latvia" , "trading centre in Latvia" .)