You may marry her in the United States or in another country, but we always recommend speaking with an immigration lawyer before making the marriage decision because not every person is eligible to immigrate to the United States.
Only US citizens may ask the government for a fiancé visa.
Permanent residents may only petition or sponsor a spouse for permanent residency and cannot ask the government for a fiancé visa.
There is a quota system for the spouses of permanent residents and this means that after you marry your spouse she may spend many months outside of the United States while she is waiting for an immigrant visa to become available.
If you decide to wait with her in the foreign country for more than six months, you may risk losing your own permanent residency so again we recommend consulting an immigration lawyer before acting.
If you have any questions regarding immigration, please feel free to call me, immigration attorney Shawn Mesa at (813) 679-5780.
Disclaimer: This information is provided as a public service and not intended to establish an attorney-client relationship. Any reliance on this information is taken at your own risk.