<p>Based on living in St. Louis, I'd recommend staying in Clayton or the Central West End. Both have tons of restaurants and parks to explore. The CWE also holds the ginormous WU MedSchool, and is on the other end of Forest Park (a DEFINITE must if you are visiting the area) from the undergrad campus. St. Louis boasts a low enough cost of living, where staying at even the Ritz is in the low $200s per night.</p>
<p>The Chase Park Plaza in the CWE is a perfect location and one of the best (if not THE best) local St Louis hotels. Even if you stay Downtown, Wash U's campus has MetroLink stops on either end... so no area in STL is more than a 15 minute Metro ride if you don't bring a car. Even the Airport is on the MetroLink, so it's completely reasonable to visit STL for a couple of days and not rent a car at all and be able to do all the main things in STL.</p>