Major first - then school. No point in attending a school that doesn’t have your major.
W&M has most majors. What do you want to study? If it’s a general bus administration degree, you likely won’t love the outcome. They offer several specializations - Accounting, Analytics, Finance, and marketing. What is your area of interest within business? If you look at minors, they have even more - entrepreneurship, supply chain, and Org Leadership.
Both of these are pricey schools - are they within budget?
Many colleges offer business and many will feel similar to these two.
Not sure why you are saying W&M doesn’t offer business. Their school is well respected as are many others.
Majors & Concentrations | William & Mary School of Business (wm.edu)