Living in St Louis, I would say for WashU you want to be in Clayton and not the city and Clayton doesn't have many good choices other than the Ritz which is expensive. I would look at the Cheshire which is an independent hotel very close to WashU or the Residence Inn or Homewood suites by Hilton both of which are by the Galleria. If you want the convenience of being right in Clayton the Sheraton is probably as good as it gets. The Springhill Suites is close also but that area is a traffic nightmare.
Re Homewood suites @
Galleria : I stayed there once. Despite the rooms are OK, I will never return. Zero soundproofing. I could almost touch the cars on the expressway and had the feeling to have a car race all night long in my room. It could be better facing the mall.
I was so tired of those bad hotels in this area and the Ritz Carlton being out of budget, I ended up staying downtown at the Hilton (near the stadium), at the Westin (but always pricey) and at the Magnolia (but some rooms are horrible there in the sense 0 natural daylight).