I say art history... just my thoughts. I think that a foundation in art history is a foundation in all of mankinds' thoughts and creations, including architecture. What do you want to eventually do?

History, engineering, urban planning, archaeology, museum studies, chemistry.... lots to choose from -- what kind of preservation work are you interested in? Research is a big part of most preservation practice, so a history minor is an obvious choice. But, if you want to deal with old structures, engineering might be a better fit. Preservationist talk about placemaking quite a bit -- planning would be relevant there. Etc.

Thank you all for all of the comments. They are helpful. I am currently at UT San Antonio, but plan to get my graduate degree and specification of historic preservation at UT Austin or TAMU. I want to do preservation design and restoration. When I am a preservation architect, I want to restore, rehabilitate and reuse old buildings. Also, unfortunately, my school does not offer any minors in engineering, urban planning or construction. 

UT Austin program focuses on architectural conservation and documentation, historic site management, and preservation planning and development. It seems to be more focused on research, policy, and planning than design. They also offer a PhD with the program for further research. Thanks for letting me know that not all Historic Preservation programs are the same. I wanted a dual MArch and MSHP and I assumed they were all the same. UC Denver and U of Maryland both have focus areas on design and Tulane has a focus on technology and methodology. Maybe those schools will be a better fit since I want to reuse, conserve, preserve, and redesign historic buildings. Tulane even has preservation studios in their curriculum. TAMU, only has a certificate in preservation, and I rather get an masters, because a masters offers more for my education. I will keep researching for different schools. Thanks for your advice.

The National Council on Preservation Education (ncpe.us) has a breakdown of all schools that offer undergraduate and graduate degrees in historical preservation. The Clemson graduate program offered in conjunction with the College of Charleston seems attractive.

What would be the most helpful or related to historic preservation or architecture? I thought business would, I am just not sure if I would like business, because of finance and accounting. I am more of a humanities and history person

Sorry, but if you want to do historic preservation you should think about acting as an owner/developer rather than conventional architect if at all possible.  Owning the building gives you a lot more control.  Developer clients have a bad habit of doing horrible things to beautiful old buildings, including knocking them down.  If you are in business for yourself, you need to know about finance and accounting whether you like them or not.  Don't just pick a minor that is almost identical to your major.  Diversify your knowledge.  Things change on you all the time.

Thanks for the website. It shows the focus areas for all of the schools. My interests in historic preservation is architectural conservation, technology, and architecture/design. According to the website, SCAD, UT Austin, Tulane, Columbia, Boston Architectural College, UC Denver, U of Florida, U of PA, U of Vermont, and Ursuline Collage has a program focused in architecture design, conservation, or technology. I want to get a dual degree in architecture with the MSHP as well, so the school has to have a good architecture program as well. Which of these schools, besides the two IVY's (It is very unlikely I would get in or could afford it) is known for a good historic preservation and architecture program. Thanks. 

Thanks for your advice geezertect. I will think about getting a more diverse minor and look into business. Some of those schools, like Tulane, has real estate development courses and majors that I can look into. Thank you all for all of the helpful advice, I will surely think hard about my minor and future grad school.