A critical element
Never, NEVER lose sight of the importance of managing upwards. You may have other priorities, but they must be kept parallel to—not in front of—this critical element. Assuming that if you can do a good job—even a great job—other things (such as your boss's approval and appreciation) will fall into place doesn't work. Remember the difficulties you have with delegation? Your boss often has the same trouble, and his/her comfort level must be constantly addressed.
Know your options
You need to listen and get an idea for what your superiors will swallow as you are listening to your staff. If you do this all correctly, you will know the range of palatable options to your superiors at about the same time you reach conclusions about what is needed. Avoid indicating to your staff any personal commitment to particular actions until this process is over.
If you really want to change something beyond what your superiors will easily go for, then of course you have a duty to present your case and try to persuade them on major strategy issues. Keep in mind, though, that on many issues of less than critical importance you will be free to decide without talking to your superiors. That is what GMs are expected to do.
Educating your boss
Even if you have a brilliant idea, you must spend time explaining it to your bosses one on one before you launch the idea in a board meeting or a senior management meeting. It is amazing how easy it is to move from a defensive position to a highly supported one by taking the time to manage relationships upward.
Make sure you anticipate, and have answers to, the questions raised by senior management. Everyone has their idiosyncrasies, and issues that you may view as minor may be very important to senior managers. It behooves you to anticipate these issues and preempt any concerns.
One thing that is incredibly important to professional success is to have good chemistry with my bosses. I have experienced terrific upward career mobility by finding, at my fourth employer, truly excellent rapport with my bosses. Obviously rapport with subordinates is also important, but you particularly need it with your bosses.
One thing to remember is that most likely you have been brought into a situation because the corporation wants change. This is a key factor to understand before you take a position. However, there are instances where you will run into opposition from the corporation regarding the recommended course of action you and your team have developed.
I have two points here. As a GM it is your responsibility to be in constant communication both up and down the line. The team is counting on you to be the advocate for the company with upper management or the board. In that light you need to have an understanding for what is salable to the organization and what is not. It is also your responsibility to do a tremendous amount of selling. In the event you get turned down for a recommended action, the only answer in my view is immediate and open communication of both the negative decision and the rationale for it. Then you need to saddle up the team and head after another objective with no delay. If it is clear to the team that you have been an effective advocate, and you communicate effectively, you will not be just "another suit."