I lived in San Diego for 9 years as an adult. I recommend North PB. BAH will get you a decent place, and having roommates means you can live within a few blocks (2-3) of the Pacific in a decent house, near surfable waves, and a 10 minute drunk walk to Garnet.
North PB is a little quieter than Garnet/Grand, and gives you quicker access to the 5 via Beryl Street.
Not to knock the earlier posts, but Mission Valley is probably the 10th place in SD that I would look to live. Guess it depends what you're looking for. Coastal is the way to go: OB, nicer parts of MB, PB, Birdrock, La Jolla, Del Mar, Solana. Coronado is nice also. There are a few cool areas near Balboa Park if that's more your speed (insert Hillcrest joke here) and the hills just east of the 5 have some views.
Some of the apartments downtown are new and nice, but you're downtown.
If you're young and single with BAH, North PB (Tourmaline, Loring, Beryl, Wilbur) will treat you very well.
North PB to Miramar was about 20-25 minutes.
North PB to NASNI was about 20-30 minutes depending on the gate.
Evenings may be a little longer, but not crazy for SOCAL.
And BTW, the best burrito in SD is the California burrito at Papa Chito's in a strip mall at Genesee and Governor. Get the red hot sauce.