First of all, central and northern Nevada in early April will be cold, possibly snowy, and muddy. Bodie will likely not be doable during the first week of April. Unless you have a snowmobile.
Belmont and Manhattan is an easy drive. I'm sure you've consulted the maps and have a route in mind. I think the main road north from NV376 is paved all the way now, I don't know as I haven't travelled its full length in over two decades (I generally have come in from the north via Monitor Valley, exit via Manhattan).
Manhattan is on a paved state highway, pavement ending on the eastern side of town. If you wish to hit Manhattan first then Belmont, simply continue along the dirt road down into Ralston Valley to the Belmont road, which is paved up into the old town.
Early April is generally a cold and snowy time in central Nevada, as elevations all through here are above 5,000 feet. Belmont and Manhattan are 6,000 feet plus.
Don't limit yourself to simply the main Belmont townsite, as over the hill to the east is East Belmont, which has plenty of ruins as well.
If you were going later in May or June, there is a great campground (free) at Pine Creek, about 15 miles north (as the hawk flies) from East Belmont. It's located just into the piņon pine belt along a heavy flowing creek with plenty of trees and willows. The Monitor Valley is a great treat to see and drive through. It's empty (except for three or four small ranches hardly visible), freeway smooth dirt road (in dry weather later in spring after annual blading) and you'll pass more wild antelope and mustangs than you will cars between Las Vegas and Tonopah.
Looking over the main Belmont townsite. The larger building center left is the former Nye County courthouse, which fell out of use after Tonopah secured the county seat very early in the 20th century.
A view northerly over East Belmont, looking along Monitor Valley. The tall stack is that of the former Combination Mill.
The Combination Mill stack and the Monitor Valley and Monitor Range. Look closely at the stack of the Combination when you visit. It is cratered extensively by large caliber machine guns by passing military planes during WW2 training as it made for a great target.
The ruins of the Highbridge Mill, a short distance south of the Combination.
If the snow isn't too deep, a tempting pathway above the Highbridge leads one to the summit of a hill adjacent to Cemetery Hill. Gorgeous views in all directions might distract one from finding a small gulch just off the path which hides four small stone cabins like this one. The view is easterly into Monitor Valley.
Now for Manhattan. This is the main drag, viewing west.
Another view of Manhattan.
I'd suggest getting hold of NEVADA GHOST TOWNS & MINING CAMPS, by Stan Paher. It's now a 2-volume softcover these days. If you can find an original, hard bound, single volume edition in your library or online (I'd try www.abebooks.com), I'd check it out as there are far more historical photos and historical facts.
I'd also suggest purchasing modern topographical map software, such as Terrain Navigator or National Geographic's TOPO! Each covers the entire state in a multi-CD set that you can load to your hard drive and view the maps in numerous views, from that looking like original paper topo maps to 3D Google Earth like flyovers, including shaded relief to the standard view of the maps to give you a better idea of the topography. And you can scroll all over the state in map view to your heart's content without having to open up single maps. It used to be that the TOPO! Nevada set retailed for $100 plus, but I got mine new a year ago for less than $50 online.