The only way i could ever see a return of battleships is in pocket form. More like the Graf Spee than the Missouri is what i mean! Here's what it would look like if my opinion was worth a damn
11,000 ton ship
600 feet long
70ft beam
To ensure the ship can move fast, why not drop in a single A1B reactor? (CVN Gerald Ford's got two). It needs to be able to keep up with the other ships.
A Composite hull of the highest quality steel for the loadbearing structure and chobham armor for the outer layer. But even that wont stop a Brahmos/Yakhont/Moskit ect...
So what do you use to make it heavily armored against missile attacks?
Massive tiles of waterproof ERA!
Navalise the technology and reduce the effectiveness of anti-ship missiles by an appreciable degree. Of course this would only be possible on the area between the waterline and the deck. Could be a hazard to crew near the affected part, but that won't compare to the damage the missile will do if it penetrates.
Moving on, two old-fashionned gun turrets placed fore with three 155mm howitzers each with state of the art PALADIN-type FCS.
The front of the ship would have the gun turrets while the rear would be allocated for the VLS and magazines.
30 Tomahawks,
16 Harpoons and/or ASROCs.
four SEARAM
two CIWS on top superstructure to suppement the SEARAM and act as last-ditch AAA
two Mark 45 54cals
four 25mm chainguns
eight OCSW .50cal machine guns
AN/SPY-3 dual-band radar from the gerald ford
RIM-162 ESSM
Give it the AEGIS system too, basically all systems from the latest Ticonderoca.
Make it a full-spectrum warship that can defend itself against any kind of threats yet cooperate and act as a force multiplier with a carrier group. It would be most of all a devastating ground-support asset.
A helicopter deck with elevator and hangar for at least one aircraft is a must! Ability to launch UAVs would be highly interesting, providing the battleship with it's own reconaissance, ASW aircraft and fire control for ground targets.
I beleive such a ship would fit well in today's naval philosophy, but in any case it would be very expensive for what it can acheive. The glorious naval warfare days of WW1/2 are over (i hope!!!) however i am sure that the mere presence of such a ship in a USCG would act as a massive deterrent against any type of attack. But i'd say any navy trying to attack something like that would have a pretty hard time.
Sorry, my mad inventor's trying to get free, plus i need to go to bed....