What with Sequestration and all, the Navy has been forced to cut numbers of CGs and cut back on CVN deployments. This post is written for a hypothetical just world where Sequestration won't happen, and the Navy is focused on fighting conventional opponents. Several decades ago the Navy wanted a totally nuclear Navy with every ship powered by a nuclear reactor. This fell through about the 1970s when reactors started to be demonized, and also the high costs associated with running reactors. However, a return is needed to the reactor for large surface warships, cruisers, and the hypothetical BBG.
1. DDGs, FFGs, and smaller. These vessels are small by definition and have to built in large quantities, and thus have to powered using conventional powerplants. Nuclear reactors simply aren't feasible because of the large numbers needed.
2. CVNs. Carrier have to nuclear powered because they have to maintain high speeds for long periods of time to launch and recover aircraft. Thus, they require nuclear reactors to supply the power needed for long sprints. Conventional propulsion is feasible, see the Midway-class, but it not the best for current CVs.
3. CGs. This is where things get a bit hypothetical. I would like to see a class of "heavy cruisers" of Long Beach size (hypothetical designation CSGN, yes the old Strike Cruiser), massive ships meant for missile warfare equipped with large numbers of VLS cells. These ships would be nuclear powered, not to keep up with the carriers, but rather for the much increased endurance and higher average speed over conventional power plants. At the same time a class of "light cruisers" about the size of the Ticonderoga-class (hypothetical designation CLGN) to provide striking power to SAGs while the CSGNs escort the carriers. These would be essentially the same as the Tico-class, but armed perhaps with a Mk 71 MCLWG for gunfire support.
Like I said this is for a just world, but this could go a long way to beefing up the Navy's AAW and ASuW capability.