North towards San Antonio, Texas
The first truck stop on the Interstate 35 out of Laredo is at exit 13, just after mile marker 12. It is a Pilot Travel Center, and the latest information is that no city bus runs that far. The farthest you can get by bus is about 4 miles before, then from ther you will have to walk, hike on the interstate (which is illegal...) or on one of the slipways (which is very ineffective), so you will probably have to catch a taxi anyhow. From downtown Laredo a Taxi to the truck-stop cost 35$ for 3 people in 2011.
Places to avoid
At night time, just like all the line between Mexico and the US, Laredo is a relatively hot spot, and you probably don't want to be outsite long after sunset. However, as a matter of comparison, it does seem much safer then Nuevo Laredo on the other side so if you have to make a choice it's probably good to be over in the US by nightfall if sleeping out. If using hotels it makes absolutely no difference.
Accommodation and Sleep
In the direction of the Interstate 35 it is possible to find camping spots throughout the comercial areas of the Laredo suburbs. At the Pilot travel center truck stop you can find good spots too, just look around! Remember to beware of nice looking green grass as this can only be green in Texas if it is watered, and that probably meens spriklers will come on at some time in the night!