Translation of German "Bolzplatz" – what's the name for an outdoor area whose purpose is to provide room for soccer/football?

In British English, at least, this is often called a recreation ground. This also seems to fit your description of being in "...bad shape, like missing turf or torn goal nets." as a lot of them are just mown fields, with basic facilities like a couple of goal posts etc.

Colloquially it may be shortened to rec or rec ground in some areas. I think this best reflects the description of somewhere where you would go just to "kick around" like you would on a German Bolzplatz. E.g. "let's go have a kick-about on the rec."

ADDITION:

@Steve – you have swayed me to playing fields, which I get the feeling is a more widely used term in English in general.

In the UK, these are generally known as "playing fields":

http://www.collinsdictionary.com/dictionary/english/playing-field

The use is not specifically for football (they are public areas that can be used for a variety of sports) although that is usually the purpose.

As an example of usage, my local council's web site provides a list of facilities in my own local area, which refers to the "Canterbury Way Playing Fields" which happen to be just outside my house.

In Ireland, we would call them pitches. In this example, you can see a list of pitches and open spaces in Dublin where people of all ages can play football: http://www.soccer-ireland.com/football-grounds/south-dublin-council-pitches.htm

In the US, since the goal fixtures are usually permanent, the areas of a park, or a park set aside for soccer, is called a "soccer field" (sometimes plural if there is more than one set of goals). If similarly facilities are provided for baseball / softball, or basketball, these are referred to as "baseball fields", and "basketball courts".

In the late 60's/70's this would be a lot. Sometimes called a sandlot. Usually an undeveloped space in a developed neighborhood (urban or suburban). This is an unregulated area (no formal field markings), usually scrap material found on site would be used for marking bases (for baseball) or goals/lines (for soccer/football).

Since the 80's I normally hear of a similar area simply called a field.