If you're looking for someplace overseas but don't want to leave the country I'd recommend Pearl Harbor, plenty of ships there. Beaches, hiking, surfing, fishing and perfect weather 12 months out of the year (by a mainlander's point of view, the locals think 60 is freezing!) not to mention many beautiful girls. Really can't go wrong with paradise. The home brew scene exist, there's at least one home brew club that I know of, probably more. Anybody who gets bored is doing something wrong. Kuaii also has a Naval base. Also another thing nice about anywhere overseas is COLA (cost of living allowance)
Out of the country. There's Sigonella Sicily. White sandy beaches and some hiking. Don't know anything about the craft brew scene. I've only passed through a few times but it looks pretty nice. I have a few friends stationed there and they enjoy it. If you want to travel Europe on your leave good oportunity. I personally wouldn't put it at the top of my list.
Yokosuka, Japan has a Naval Base. Japan is okay. They do have beaches and hiking. If you happen to get stationed there you have to climb Mount Fuji. There is another base I know of in Sasebo Japan.. It's been 25 years ago but I would not step foot back at that place. Not much there to do.
Cubi Point in the Phillipines was a place to beat all other bases but it has long ago closed up. Much different Navy and world back then...
As said above San Diego and surrounding area very nice. There's a lot of outdoor stuff to do and the weather is beautiful all year long.
Best of luck in your Navy career!