You can now write post utme in schools which you did not choose as your choice. Once you scored 180 and above, you can easily apply for the post utme exam by obtaining the form from such institution.
You can see the lists of such institution that accept students who score 180 and above at ngscholars site for more information.
I only know of this great institution, Olabisi Onabanjo University (OOU), Ago Iwoye, Ogun State.
All you need to do is for you to go down to the school to obtain the post-utme form using your ATM card at the POS terminal located in the school campuses (Ago, Ikenne Etc).
The form is Six Thousand, Five Hundred Naira Only.
You will be given the post utme scratch card which you will use to complete the online registration.
Visit the school site on http://www.oouagoiwoye.edu.ng for more details.