I would think that there would be more than just small 1 BR and Studio apartments in the Central West End area. Do you want 2BR? I'm sure you could find some to suit you.
On Craigslist the University City area has plenty of listings for 2 and 3 bedroom homes.
st louis craigslist > apts/housing for rent: search for "university city"
Some more details about exactly what you're looking for would be helpful.
If you still can't find what you're looking for Central West End the University City area is nice, as is Clayton, and Downtown, but they might be too noisy for you.