When I went Newport to SD, I took I-95 down the coast to Jax, then I-10 all the way west. Looks like it's out of your way on paper, but the time diff isn't all that much. And then you get to see the big Gulf and East Coast cities.
I don't know if you've always been in Cali, but the change of coast is like going to Canada...it's mostly the same, yet everything's slightly different. And you should be able to count on good wx (or at least, no snow) for the trip.
San Antonio's a good place to stop. Nawlins can be interesting if you've got a day or two. Swing through P'cola, visit the Museum to get some Naval Aviation moto-juice and have a steak at McGuire's.
From there you can either head up through ATL or go on to jax; I recc the latter. Saint Augustine is a detour, but if you've got the time, it's interesting. Savannah and Charleston are along the way and GREAT cities to visit.
When you hit Virginia, go through Norfolk, so you can see why you don't want to be stationed there, then go across the Chx Bay Bridge and up the Eastern Shore instead of through Richmond/DC. Beautiful drive, no traffic, and time's the same. The Bay Bridge has a redonkulous toll ($15 last I was there) but it's cool enough to be worth it.
If you have extra time, the Cape May - Lewes Ferry goes from DE to Jersey across the Delaware River. Takes about three hours to cross, but nice trip and allows you to miss a big chunk of the Jersey Turnpike.
Getting through NYC sucks, though I had good luck crossing the GW Bridge at Ft Lee and then continuing up I-95. You miss pretty much all of the City traffic. From there, straight shot across CT (nothing worth stopping for; Mystic's nice if touristy) and into RI. The Kingston-Jamestown shot to Newport is back country roads.
Then go out and get shithoused if that's your thing, or at least have a great big dinner. Last fun you'll have for a while, and Newport's got some great pubs and restaurants.