These patterns express purposes of motion(e.g., going, coming, returning). The purpose, which is presented in the V(ます)form, is marked by the particle に. Verbs which follow the V(ます)に phrase are motion verbs which express a movement from one place to another.

These are basically "Place へ 行く(go)／来る(come)／かえる(return)" patterns with the V(ます)に phrase inserted between the destination and the motion verb. Therefore, the place noun is marked by へ, not で.

I'm going to the cafeteria to eat.