Welcome to RTA!

The best thing to do to find suitable hotels is look at the Interstate exits outside of town, ones that also have a truck stop/travel center (TA, Pilot. Flying J, Petro, Loves) at the same exit. They will generally have a "back lot" suitable for trucks. Call the hotel to confirm.

Now, for your routing. I assume you mean Monroe, LA?

You do NOT want to take I-95, trust me. Take I-78 out of NYC to I-81 in PA, then take that to I-40 (use the I-640 bypass around Knoxville) to I-75 to I-24 through Chattanooga. This does NOT take you to either Winston-Salem or Nashville, neither are anywhere near the most efficient route. From Chattanooga, take I-59 to I-20, using the I-459 bypass around Birmingham.

Your first 2 overnights should be near Wytheville VA and Meridian MS. Both should have a good choice of truck-friendly lodging.

There will be no clearance issues on any Interstate highways.

You can use our Hotels app to research hotels and even book them if desired. If you click on Hotel Description, it will generally say if they have a truck-friendly parking lot. For example, the Days Inn in Wytheville says this:

A spacious parking lot means plenty of room for large vehicles such as trucks and RVs.