What particle should be used for a place of action (or a place to go?) in case of using V-2+に行く construction? E.g.
食堂 ＿ 食べに行きます。
At one hand, 食堂 is a place of action (eating) and で-particle should be used. At the other hand, it's a place to go, so に-particle should be used. However, the last case seems a bit strange to me, because a verb 行きます already has an object with に-particle - 食べに.
So what's the correct particle to be used in such cases? Maybe both particles are acceptable? - In this case does a choice of particle carry any meaning?