I agree with all the others have said. All the schools in Texas are good. People will KILL TO GET into one of these schools. After trying several times, I've finally been accepted to one of the 7 TX med schools.
Anyway, I have a passion for missions esp. Africa. There are organizations (I only know of one right now) out there that offer scholarships/loan repayments to med students and residents who are dead-set on going into medical missions. It is like the army/navy scholarships. They will pay tuition for you in exchange for an agreement to be a long-term missionary. If you default, you'd have to pay them back. PM me if you need more info.
As someone who attends a Texas med school and is going into pediatrics, I would fully support your idea of going to a TX state school. All of the schools are good, and some of them top in the nation. There's no need to incur extra debt to attend a private school out of state.
If you have particular reasons for wanting to leave TX (are there such things? kidding!), then apply widely and see how you do with financial aid.
As for applying to residency in pediatrics, doing well and getting good letters of recommendation at any school in the US will make you a good candidate for residency.
"All you have to decide is what to do with the time that is given to you."