Looking for a mosque to marry an interfaith couple

My fiancé’s Shia Muslim family has requested that we have a marriage ceremony in a mosque. Neither of us feel strongly about religion, but are willing to accommodate their wishes if reasonable.

As I understand it, Muslim men can get married to Christian women. I am from a Catholic background, so conversion would not be necessary. I would also personally prefer to stay as non-religious as possible.

Are there any mosques or Islamic institutions in Houston, that would be able to marry us? I’m still educating myself about Islam, but am hoping to find an open and progressive religious leader to guide us. edit: His family is not from the area, so I'm doing some preliminary research. It'd also be nice to have some control over the process.

I’m also open to hearing general advice from interfaith couples (or, more accurately, couples with interfaith families)!