What is the best country in the Middle East in terms of exploring renewable energy potential?

The United Arab Emirates.
Abu Dhabi is doing a great job at this through its clean energy company and research center, "Masdar".

I am proud to say that, the biggest solar-power project in Abu Dhabi was handles by one of our consortium companies.
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However, the answer to this question would simply be.
It depends on the govt.
renewable policies, investor friendliness and ofcourse resources available.
UAE, i would say.

Jordan is the first country in the middle to have a dedicated renewable energy law with defined feed-in tariff and instructions.
Renewable energy projects are now being installed at businesses and private residences with pay-back-period of less than5 years.
Jordan has excellent solar energy potential combined with high energy prices.
This makes renewable energy projects financially viable with short pay-back-periods.
Recent renewable energy law now allows customers to export excess generated energy to the grid boosting profit from these installations.
Jordan had already been a leader in the use of solar water heaters decades ago and is now leading the newer generation of renewable energy technologies.

الامارات العربيه المتحده

UAE SURE , THE BIGGEST SOLAR PROJECT IN THE WORLD IS IN ABU DHABI

Dubai, & sharjah where electricity cost is3 times higher than abu dhabi

KSA and UAE are emphesized on renewable energies and doing further research on reneable sources along with application

المملكة العربية السعودية

As the environmental aspect of UAE is hot humid . therefore the solar profile of the region will be best for solar power generation. but as in vast territories uncovered with buildings the wind profile will be better as well so we can use wind generation as well. also the waste production generation like biofuel, fossil fuel generation plants can be used. because the cities are well planned for its sewerage system to collect the waste products.

It's Egypt, and specially Gulf of Suez - please check the annual report of the global wind energy & also check Wind Atlas

The biggest solar project in the world will be in Morocco2000MW untill2020.