Hello Y.J., pemerintah kota is the government who governs the city such as governor, etc. while balai kota is a place where the public staff work for the government. I hope it helps.

pemerintah kota = the city's government authority, the people. balai kota = city hall, the place.

I can help you in learning Indonesian. I'm still figuring out to set up the paypal account. After that, I can help tutoring you if you're interested. I'm looking forward to talk with you soon. Thank you.