Oh, my commiserations. No, it's not that bad, and early October can be quite pleasant to visit St Louis, weather wise.
It is certainly worth a visit to the Arch, you can catch a "tram" up the inside of the Arch to a viewing platform at the top, looking over the city and Mississippi, however no good if you are claustrophobic. Another popular attraction the Budweiser brewery which does tours of the historic brewery.
If you have a car, the Botanic Gardens and/or Forest Park can be quite pleasant. Forest Park is a large park area towards the western part of St Louis. Site of the 1904 World Fair, there is the Missouri history museum (some of it quite interesting), gallery and a reasonable zoo - all free. Also can rent bikes to ride around the park if that takes your fancy - it takes about 2 hours.
Other areas of interest include the historic Soulard area - has a good market on the weekend (not sure if open on Sun afternoon), "The Hill" for Italian food, Central West End for cafe culture, Washington Ave where people are leaving in renovated warehouses and thus some OK cafes and bars.
