I try to come over once a year (have to get to London for work, so I take a day or two to come up). I've always enjoyed right about the penalty spot or the penalty box line on the side closest to the away supporters, maybe 20 rows back in the lower level. Can see the pitch; cost is good; best combination of a decent view and you can hear all the best banter. I've sat in the padded seats center pitch on the second level (which cost more) and the upper level but the atmosphere isn't quite as good. Haven't done Hospitality. Others will have good advice on tickets but I just go through the club as a Citizen member or whatever its called.
Have to watch the fixture list closely because of the rescheduling for TV, which means if you book early you have to have a window of days (Saturday-Monday; Friday too now I guess) in case the fixture gets moved. Others will know better but Sky gives everyone about six weeks notice I think. I got burned on that the first time I came out and had to change a non-refundable flight which sucked.
I concur with those who mention the Radisson. Make sure you hunt down a few pubs before the match, and Mary D's. If the City Store at the Etihad is a zoo try the one in the Arndale. Take a gander at the National Football Museum when in town and the Museum of Science and Industry, among many choices. If you have an extra day take a day trip to Chester or York or just walk around town.
You'll find City supporters the best people around and always helpful and friendly to others, even us Yankee tourists. One non-negotiable: learn the songs, drink lots beforehand and sing with gusto. Our American accents get drowned out in the cacophony so no one will know you aren't a Manc :)