For inexpensive lodging, look to the budget motel chains such as Super 8, Econo Lodge, and my personal favorite Motel 6. For two people, plan on spending around $60 per night, maybe more in some places depending upon what local events may be occurring.
Places to visit include, but are not limited to:
The Grand Canyon National Park, Arizona.
The Cadillac Ranch, Amarillo, Texas. (You just have to see it to believe it.)
The Alamo, San Antonio, Texas. This is the site of a pivotal battle in Texas' war for independence from Mexico.
The Johnson Space Center, Houston, Texas. This is the control room for NASA's manned spaceflights.
New Orleans, Louisiana, if for no other reason than to assure yourself that it really does exist. Seriously, it's a good place to visit, except possibly for the Lower 9th Ward.
Orlando Florida. This is home to Walt Disney World, Universal Studios Orlando, and Sea World Orlando.
Kill Devil Hill, North Carolina. This is where the Wright Brothers made their first successful powered flights.
Washington, DC. Here, you will find the museums of the Smithsonian Institution. You could use up your whole 90-day travel time just exploring these.
I've been to a few of these places.