You can appoint a guardian, or write in anything regarding the guardianship of minor children into your will. That being said, if you fail to name a guardian, and you die with no other relatives to place the children with, then the court will look to blood relatives before anyone else. It would seem obvious that you'd name a guardian, if you're going to write in who you don't want your children with, but I felt I should mention this since you brought up the event of not naming anyone.
Most people who set up a guardianship arrangement have second, and even third choices in place if the first choice is unable to fulfill that great obligation (along with trusts in place for their care and comfort). If you didn't have anyone named, or everyone you had named could or would not do it (one should always get the assent of the named guardian prior to naming them and work out financial arrangements) the court would take your wishes into consideration as a factor to consider, but it is not bound by them. If there is a family member who wants or is willing to take the orphaned child(ren), than It is always seen as better, in the absence of a pre-arranged guardian or clear proof to the contrary, to place children with family as opposed to strangers.
When there is no plan in place, the placement is considered temporary while DHS/DCF investigates the situation and makes a plan for permanent placement. I am assuming you are not talking about disavowing the other parent – unless they've had their parental rights terminated for abuse or neglect. If there is a living parent, even if you have full parental rights and responsibilities, that is who the child will be placed with unless that person cannot or will not take custody.
Assuming you're not referring to a parent, as with any court action involving children, a "best interest of the child" analysis is undertaken, and in a case like you're describing, many factors would be analyzed like fitness from a non-biased perspective (a guardian ad litem is appointed as well as a child services case worker) with frequent visits and interviews, background checks, well-being checks, and the like before any permanent placement order occurs. Also, if the child(ren) are older, they will also be heard as to their preference for placement if there are competing interests. Again, this all assumes you didn't name a guardian who was willing to take custody, and the other parent was also deceased or barred by law from taking custody.