I thought I replied to this earlier, but don't see my reply, so here it goes again. Multiple people have recommended Buffalo Bill State park which is 10-15 miles west of Cody. We did a quick drive by from there as we were leaving Yellowstone on our way to Thermopolis 2 years ago, and would certainly consider it if and when we are in the area again. If you are in the area and have any interest in dam construction you should visit and tour the Buffalo Bill Reservoir dam, it is one of the oldest large concrete dams in the US, when we were there they had shuttle golf carts from the parking lot to the visitor center, so don't let the potential of a long walk scare you off.
Ike
p.s. Just so you are aware Buffalo Bill Reservoir, is an irrigation reservoir so the lake water level varies considerably depending on the season, it also is not a particularly pretty lake, in fact it is a bit ugly, the water tends to be muddy and there is little vegetation around it, instead it is mostly barren rock.