A chore any foreigner staying in Beijing (and the rest of China) has to go through is getting registered at the local police station within 24 hours of arrival at your new place of residence even if it is just for one day. This means if you change apartments within Beijing you are actually required to change your registration every time. The official stance is that it is in the interest of the foreigners to do so, just in case something happens to them. One may then wonder why not all that many other countries feature similar laws. You may even get fined if you are not in compliance, although I have never heard of anyone having it happen to him or her.
Showing the way
If you are staying at a hotel that is allowed to admit foreigners (be aware that not all hotels are) the hotel front desk will take care of all the formalities for you. So you can spend more time taking in the sights and food. If you are the personal guest of the Chief of the Beijing police you probably would not have to bother neither but I take it you are not.
The Grand Hyatt Beijing, I have never slept here but they can probably allow foreigners in
The police registration process
Take your passport and rental contract (if you are staying with a friend your friend’s rental contract; if you are staying with the home owner proof of ownership) to your local police station. The process is not 100% standardized so some police stations may ask you for photocopies of your passport and passport photographs. Also, while getting registered in Beijing is a straight-forward yet slightly annoying process, you may run into police that has no clue how to go about it if you try to get settled in the smaller cities. It is simply a problem of experience and you are best advised to stay polite and patient. Getting angry will get you nowhere. You will be issued a white slip of paper at the end and then you are home free. Congrats.
The fruit of your efforts, you are finally registered