Good Morning, David,
Several things occur to me regarding the Arch. First, it is huge, 630 tall and 630 feet from leg to leg. The Arch grounds look much better now than in earlier years because many trees have been planted and have had time to grow. If you don't want to include the whole structure in a photo, there are all kinds of different positions to shoot from. One location far enough away so that a "normal" lens works well is the steps of the Old Courthouse, which is several blocks from the Arch. A Fourth of July fair draws thousands to the Arch grounds and causes some wear and tear, so shooting in early to mid-June has advantages. Shooting from the observation room at the top of the Arch is possible, but the angles are limited and the windows (not exactly fine optical glass!) will somewhat degrade your images.
To shoot the Arch and the city skyline, there is really only one best place. The Eads Bridge, which crosses the river just north of the Arch grounds, has a pedestrian lane/bike lane on the southern side. It's not very wide, but there are widened spots over each of the bridge piers; each location has enough room for at least two or three people working with tripods. The use of this pedestrian/bike lane is not usually heavy. There is normally only rather light vehicle traffic on the bridge, and heavy trucks are relegated to other bridges. I have made time exposures of several minutes from Eads and had no problems with traffic-generated vibrations. The position above the eastern-most pier is by far the favored one. Even from there, the Arch is so tall that a leveled 35mm camera with a 50mm lens will cut off the top. A 40mm or a 35mm lens should work out OK. (I find that a 150mm on 4 x 5 is fine, but it takes about 3/4" front rise to include the top of the Arch.)
The St. Louis Zoo is an obvious attraction. It's free, but parking in the Zoo lot is at least $6-8. (Haven't been there lately, so I'm not sure about the exact cost.) If you arrive early, there is free parking north of the Zoo on the road leading up the hill to the Art Museum and other adjacent park roads. In the summer most of the spots near the Zoo will be taken fairly early.
Shaw's Garden (officially the Missouri Botanical Garden) in south St. Louis is worth a visit. There is an admission charge (there may still be one day a week with no charge), but parking is free. This is a location which is really a natural for color film.
Many nominally east-west streets in St. Louis actually run slightly southeast to northwest. For at least six to eight weeks in June/July, there is early morning sunshine on the "south" side of the street--something which I've found very handy on several occasions.
Just to the southwest of St. Louis is the National Museum of Transport which has a large collection of steam locomotives and other railroad stock. It's worth a visit, but the locomotives are parked fairly closely together and shooting angles can be somewhat limited. I've found that a cloudy day works best here, because in bright sunshine the mostly-black locomotives turn into very high-contrast material. Flat lighting and slightly-extended film development will work better.
This is only a brief intro, but perhaps it will give you a starting point and raise some other questions. Again, I'll be more than happy to respond to a PM with a lot more detail than may be of interest to everyone else. I spent much of several summers shooting the St. Louis area for a local stock agency, so I'm familiar with a lot of other locations, both in Missouri and Illinois.