The correct choice is '食べ' (stem form of '食べる' - to eat). The grammar pattern '[Verb Stem] + に行く/来る' expresses purpose of movement (go/come in order to do X). Sentence context: '...we went to a nearby restaurant in order to eat delicious food.' Therefore, '食べに行きました' is correct. The other choices ('食べて', '食べる', '食べよう') do not connect with the motion purpose particle 'に'.