Went through there in April on my way back from Lees Summit. I recommend taking I-84 to I-684 over the Tappan Zee to I-287 to get around NYC metro.
Then I-78 and I-81 Hagerstown (this avoids the Penn Tpke), then I-68, I-79 and I-64 to the I-255 loop around St Louis. I-55 south from there takes you to Sikeston. Plenty of campgrounds along he way. We stopped at the KOA in Sutton WV (part of a Days Inn), Elkhorn in Frankfort KY and Rend Lake in southern Illinois.
You could get to the Tappan Zee from Swanzee using I-95, but it is a miserable road. The only time I'd do that is a Sunday morning. Take I-95 to CT9 north to Middletown, then CT66 to I-691 to I-84.
You could also stay on I-84 to US 209 to I-80 and pick up I-81 north of Harrisburg, or stay on I-84 to Scranton and pick up I-81 there.
Jerry & Jeanne
1996 Safari Sahara 3530 - 'White Tiger'
CAT 3126/Allison 6 speed/Magnum Chassis
2014 Equinox AWD / Blue Ox