A US citizen and I plan to marry: can we have the wedding here in the Philippines?

You can have the wedding anywhere you wish. Just be aware of how it can affect your plans. Do the both of you want to continue living here after the wedding? Or do you want to move to the U.S.? If so, how soon after the wedding? In any case, where does the US citizen live at present?
This is because if the US citizen is living in the Philippines when you get married, the immigrant petition based on your marriage can be filed at the US  embassy in Manila. The two of you can then be together while waiting for the papers to be processed, and the both of you can travel to the US at the same time once the process is complete and the immigrant visa is issued. Upon approval, however, the immigrant visa granted by the US embassy will have to be used within six months of issuance. But if you do not plan to immigrate to the US soon after the wedding, the immigrant petition can be filed later. Another thing to consider is that US immigration laws require that the US citizen petitioner must be residing in the US to execute the required Affidavit of Support. If the US citizen is not currently residing in the US, he or she must  establish to the satisfaction of the US consul the intent to go back and live in the US. Now, do not forget that even if you do immigrate, you can still go back to the Philippines. If you do go back and you plan to stay for a while, you should ask permission from the US Citizenship and Immigration Services by obtaining a re-entry permit. This will prevent the loss of your immigrant status (or green card) due to abandonment.
If the US citizen resides in the US, then the immigrant petition must be filed in the U.S. after you  get married. Unfortunately, while spouses of US citizens are immediate relatives who always have visas available because they are exempt from annual quotas, the process itself can take from 6 to 12 months after the petition is filed. Hence, the two of you will be separated from each other because you will have to wait in the Philippines – although the US citizen should be able to come and visit anytime.
Sometimes, a K1 visa might be better. This visa is available for the fiancé /fiancee of a US citizen. It is a nonimmigrant visa ( not an immigrant visa) given to a person who is coming to the US to marry a US citizen. Thus, people who are already married cannot qualify for a K1 visa. But if you are not yet married, obtaining a K1 visa takes about half the time it takes to get an immigrant visa – 3 to 6 months from the filing of the nonimmmigrant petition. Unfortunately, this means that there cannot be any wedding here – not a church wedding, not a civil wedding. Do remember also that there is no such thing as a “secret” wedding. (There is a special kind of K visa known as K3 for those already married to US citizens and have pending immigrant petitions, but currently the immigrant petition is still processed first even if a K3 petition is also filed.) 
However, once you have the K1 visa, you can come to the US to marry the US citizen. In fact, you have to marry the US citizen who filed the nonimmigrant petition for your K visa within 90 days of your arrival in the US. If you marry any other US citizen, you will not be able to get any kind of immigrant status – you will have to leave the US. 
So if the US citizen you are going to marry does not live in the Philippines, you have a hard choice to make. If you marry here, where most of your friends and family members are, you will wait for about a year after the immigrant petition is filed before you can immigrate to the US as the spouse of a US citizen. If you marry in the US instead, and you get a K visa here, you will be together in about half that time – maybe even shorter. But many of the friends and family members you’ve always dreamed of being in your wedding will probably not be able to attend.
You will have to decide for yourself. I hope this helps you somewhat.