Hi Cara,
Around your questions on the various areas of the city, I generally find the west side of the river to be a bit more favorable. Also, the various townships seem to be easier and friendlier to deal with than the City of Bay City.
In the City of Bay City, the utilities (water/sewer/trash and electric) are managed by and paid to the City. Natural gas is thru Consumers. The base rate for the utilities thru the City is about $75/month with no usage at all. Also, the building and permit department for the City is difficult to deal with. The townships have much more liberal policies.
Rentals seem to get filled pretty quickly in my limited experience.
I have a great home inspector to recommend to anyone who might need one. I also found a great electrician. Those are the only 2 providers that I can really recommend as the others I've dealt with have not been worthy of recommends!
My history is that my family comes from Bay City, and I was born there. I spent part of my childhood there, and I have pretty much my full extended family there. Two years ago, I bought two houses on one property from my grandmother's estate that my grandfather built in the 40's and 50's. The property is in Bangor Township. Both houses had a lot of deferred maintenance that I have taken care of. Then last year, I bought a bank foreclosure on the East side (in the City of Bay City). It was a great price, but needed quite a bit of work. That work is finally finishing up, and I will sell the house in a month or so. It's been a long road.
Please let me know if I can help any more.