BTF 024, always good to have interim and long-term goals, good for you to get excited about all the great possibilities. Believe Navy P-3 squadrons still deploy/rotate through NAVSTA Rota Spain. Wherever the Navy has OCONUS bases, it's possible to have resident squadrons but I'm not sure what's where anymore. Aviation squadrons and dets, both fixed wing and helo, deploy with Navy ships all over the world to some great port calls. Ahh... Phuket, Thailand; Hong Kong; Pearl Harbor; The Med; Acapulco; Panama Canal transit; Rio....
The "needs of the Navy" (and Marine Corps) will influence all your chances at anything. If you service select Navy air, if you do well at flight school, if there are slots for the P-8 pipeline, if you are high enough in your flight school section to get one of those slots, if, if, if.... but all good stuff to shoot for by working hard at each stage as it comes along and being open to various options. There is some good reading on other threads here about "chances" of doing various things.
Don't believe we do any flight training overseas, but do have Navy flight students in the joint Navy-AF program at Vance AFB.
You will get plenty of briefings at USNA about opportunities for semesters abroad (just 1) and summer training blocks. Midshipmen also do many of the NOLS expeditions in the summer. You will be tied firmly to Mother B (Bancroft Hall) for most of the academic semesters, though, because USNA has a mission to ensure you are trained for anything the Navy or Marine Corps needs you for.
One of the best things about Navy life is the opportunity to go places that pop up out of nowhere. I "had to" go to Monaco for a month as a single LT when the Navy sent a USNS hydrographic ship to the International Hydrographic Conference -- every seagoing nation in the world sent a ship. Met Jacques Cousteau, went to a different nation's shipboard reception every night. I also "had to" spend several weeks at the Peruvian Naval Academy in Lima in the late 90's, the year before they brought women in as cadetes, to assist with staff briefings on the transition, using USNA's experiences and practices.
Be assured you will see the world, from the beautiful and exotic to the dangerous and ugly.