I am trying to do a cultural project on the city of Harbin. However, I'm not sure if it is correct to say this. I found out that Harbin was the capital of the province of Heilongjiang. If I said, 哈尔滨是黑龙江的首都, would it make sense since 首都 means capital.
No, you should use
省会 (provincial capital) instead, i.e.
哈尔滨是黑龙江的省会. You could also use
省城 (in a little old-style), or
首府 (especially for
首都 is only used for the capital of a country, e.g.
I am afraid it is not very suitable, 首都 is capital，Beijing is the capital of china, the capital of province is 省会，guangzhou is the 省会 of guangdong province.