Some incorrect info here. The Wuksachi Lodge is up in the higher part of Sequoia National Park, above Lodgepole. You might see if they have vacancies for your dates. Not a bad place. If you want to stay in Kings Canyon, your best bet would be Grant Grove or down in Cedar Grove, although Cedar Grove is pretty rustic. For a place just outside Kings Canyon Park but in the mountains, check Snowline Lodge along SR 180 from Fresno.

If all else fails, there are a couple of basic hotels in Three Rivers, which is not really up in the Park but is along the Kings River, in the lower mountains below Sequoia. I know of a Comfort Inn and have seen another lodge or two along the highway - SR 198 from Visalia.

Both Parks are, as indicated, connected. You can (and should) drive between the two via the scenic General's Highway.

Silver City is not really a place I'd recommend.