You are going to need an older vehicle to meet that price. Look for a Corolla with low miles. Not sure which years, but I was told there was a period of several years when Toyotas were being made here in the USA that they weren't very reliable. My '88 Camry had 325k on it when I junked it. My '94 Sentra had 294k when I totaled it. I did nothing to the Sentra but change oil, tires, brakes and rotors. Same for the Camry except it didn't have a stainless steel exhaust system so it required new muffler and exhaust a couple times over its life. The automatic transmission in the Camry was starting to slip when cold. I never touched the transmission fluid. Sentra 5-speed never needed work.
As luck would have it, I just helped my daughter get a vehicle. What she wound up with was a 2003 Forester with just over 136,000 miles. Total with everything came to your budget. Rebuilt title, but we got lucky and happened upon a small, local dealer that specializes in Subarus. Doesn't advertise. Strictly word of mouth from happy buyers. Three generations of families buy from him. Apparently Subarus need the timing belt changed at around 170k miles, but otherwise are very reliable. Daughter got to drive it in rain the first day she had it and loves how well it handles wet roads. She also has a 3 year old so safety is paramount.
It pains me to say this because I work in manufacturing and take extreme pride in doing a great job, but I would hesitate suggesting any American made vehicle. My '04 LaSabre was the nicest car (and most expensive new) I've every owned. However, the $179k miles (when I had to get rid of the LaSabre) on the more expensive American made car cost me more than the total monetary output of the 614k combined miles on the 2 previously mentioned foreign made cars. A sad reality that depresses me as I would prefer to buy American. To be honest, I would buy a Hyundai before I'd buy American.