On the first day of our freshman year engineering physics intro class, my friend Bill told the Intro class that he wanted to get a commercial pilot license while he was doing the engineering degree. Everbody laughed because they assumed the EP program was too difficult as it was....
He did, in fact, finish with a degree in aerospace engineering and his commercial multi-engine pilot license.
I would suggest Embry-Riddle Aeronautical University in Daytona Beach, FL...they have one of the most respected flight programs in the country, and the engineering physics and space physics programs are very good, as well.
On a side note, their aerospace engineering program has been around number 1 in the country for the past several years among universities that don't offer PhD's.