well, not an bad effort at all. a few things come to mind first of all, loose from the powerplant.
- it might be an idea to fit AGS-Lite, if shore bombardement is not the main reason of existance for this ship
- I wonder why the Mk 57 PVLS is not used?
- the SPY-3 + VSR have 120 degrees angles instead of the 90 degrees of the SPY-1, so you only need 3 instead of the 4 drawn right now.
- nuclear ships are known to be quite a bit bigger then dinosaur powered vessels with the same systems.
in arrangement, she looks about right.
then, the parts. note that the steam turbines you have used are 1930's vintage, so I would look into newer ones. I have a set of gearing class turbines drawn which are slightly newer (PM me if you want them) but I do not know if it would be more usable.
seein the position of the aft turbine room and the electric engine room, I cannot see why you would not pu them in the same room, and maybe even directly couple one of the reactors. by putting the electrical engine to the gearbox you can run both shafts on one reactor or on the gas turbines, or deliver power to the onboard power network (IEP) with an shorter machinery setup.
the post you made later (after I started writing this) fixes that though, but keep it in mind 
if we go a bit into handwavium, we can say that was the D2G developed further, it would have gotten more power out of the same size. that, and the fact that turbines got better due to computer aided design, we can assume 35000 shp at least, maybe even 40000 from each reactor.
the zumwalt has an immense amount of power available, but not all of its engines will be in operation all the time. if we look at an normal (non nuke) mission profile, we see that ships stay at low speeds quite a lot. in that view, I think that CONAG would not be that inefficient at all, as the gas turbines would only be started when required. it would make sense to have some smaller gas turbine and diesel sets as 'regular' ship service units for when the ship is not under propulsive power(or when at really slow speeds), so both the gas turbines and the reactors can be shut down if they are not needed.
a longer waterline might result in a lower required power as well, so I personally think you need the power of the zumwalt as a maximum, not a minimum. (the virginia had enough with the 2 D2G and the ship service generators, of course there was less power required for the systems back then but even so, doubling this amount seems excessive even 50 years later.
now, the ship design. you need to look at your mission profile. what speed will you be sailing on most of the time? that is what you optimise the hullform on, and this defines the length (hull speed)
this is reason one why DXGN (virginia) is so much longer then DXG (kidd) (the other is the displacement due to the weight of the reactors) you might end up with a bigger ship then the zumwalt if you want to go 30 knots all the time.
after you have determined that, the next problem comes alive. on first glance, there are maybe 4 or 5 heavy systems on board: the radars, the VLS, the gun, the reactors and the hull itself, for example. the hull itself has its center of gravity about midships, and you want the weight of your entire ship in about the same place, as that gives you an effective hull form. as the weight of your propulsion system will end up on about 25% of the entire ships weight in this case, and you have very little fluids on board you can stabilise the ship with, this determines the place of the reactors. you can separate them from each other, but the midpoint between them should be about midship.
the superstructure where your gas turbine is in should not neccecarely be as high as that where the radars are in. hell, those things are light and you can move them around in this case, so you can put them under the helideck if you want. do not ever let them be a hindrance for where you put your reactor acces channel.this might shorten your superstructure quite a bit too, so you might be able to be a bit more effective with your space. the width of the ship might make it possible to have PVLS next to the reactor spaces, if you want.
note that your freeboard looks quite high. lowering it one deck already gives you one less deck to move the reactor trough. that said, as long as your stability can take it, there is nothing wrong with more freeboard
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