でAt, In

で is a particle that has several different uses in Japanese. At its core, it is always used to highlight something that is 'required' to perform some sort of action. One of these uses relates to places, and translates roughly as 'at', or 'in' in English.

In these sentences, the place is considered essential for the action to be performed, or the result of the action to be achieved. This is unlike the particle に, which marks the location itself as being the destination or target of an action. Basically, で means (A) 'place' allows (B) 'action' to occur. While に means (A) 'place' is the target for (B) 'action' occurring.

In the first example, we can see that に marks the place that the person exists during an action, but the action itself is not dependent on the place. In the second example, the action is considered dependent on being at that place, as there are possibly no barbeques in other areas.