You don't only pick the right institution due to your JAMB score, there are other things you will want to consider.
1. The course you like to study. Not all institution offers the course you want to study!
There are some courses that are offered by very few institutions in Nigeria. Eg Criminology.
I think there are just 5 universities that offers this course. Not all institutions offer all courses! Dont go and want to study Nursing in a tech school. Make your research.
2. Your pocket. Some universities are generally more expensive that the other. Unilag and LASU for example have very cheap school fees compared to other schools. If your parents aren't really financially buoyant. You shouldn't consider choosing an expensive school.
3. School fees and other departments fees of the supposed school.
4. Distance: perish that mentality of I want to go far away from home. it's rubbish. I live in lagos and also school in lagos. there's nothing like disturbance. My parents can't come to my hostel to drag me. and I'm very free in school, so that idea of running far from home is bad. I'll suggest you school in your state, the poor security in Nigeria should be enough to teach you that you need to be close to your family.
A lot of killings here and there, a lot of kidnaps I the road. Personally, I'll not advice anyone to go too far from home. It's a bad mentality. You can be in your state and have fun. the worst is to go to a neighbouring state. Eg ogun state and lagos. These state are not far from each other.
So, try to stay close to your family.
But if you still love the idea of going far away from home or travelling, then do what's best for you.
5. Your family beliefs. Some families generally have some beliefs, so you should consider it too