People in the US drink in the parks, the suburbs and the cities, especially in the evenings. The care and discretion one needs to take is proportional to how much free time the cops in the area have and circumstance / setting. You can drink openly at the beach. If in a small town park, you'd want to either have the alcohol in an unmarked bottle, a soda can, or a brown paper bag. In the cities the cops are typically concerned with real crime that they do not care and one can almost openly drink. In some areas one can legally openly drink, like in Las Vegas.
Access to alcohol is a separate thing altogether, and is freely available depending on county and state, but, in the areas where the majority of Americans live (ie, not Utah, or similar), it's very easy to get alcohol and it's not seen as a bad thing.
The issue is that the US is so large and disparate that everyone's experience will be slightly different, and, no offense, but your opinion of drinking culture in the US seems off base and I get the sense you don't know what you're talking about.