Yale is a great school, but for your post-MBA aspiration, Yale should be out of consideration given your other choices.
Here’s a great guide to energy, written by a GC Legend:
riverripper-s-guide-to-energy-76849.html?hilit=energyOne question to consider, do you currently work with energy in your IB job? If you do, you can make a convincing argument for O&G come recruiting time, wherever you go, as long as the company recruits at the school. If you don’t, going to school in Texas would make a difference.
I’m not familiar with O&G, so I’ll offer some general advice.
1) I think it would be hard to get a corporate development role being an international. The visa sponsorship issue is just too difficult for most companies. However, some company may hire you as a global candidate and rotate you through the US. I would recommend contacting the student clubs to understand better.
2) UT is probably the best school for O&G, due to the strong alumni base and its great location. I do not see Rice surpassing UT in the near future. I heard they are building a new building for MBAs only. You may be able to enjoy it in your SY.
3) Chicago would be a great school for post-MBA opportunities in general, not specific for O&G. The top consulting firms hire for the Dallas/Houston offices (strong energy practice) out of Chicago, which is not the case for UT (but I bet UT places very well for the non-MBB firms).