。
The problem was where to have lunch.
Literal
Problem [topic-は] where [at-で] lunch [obj-を] eat [Q-か] [copula-だった].
The particle で marks the location where eating happens (an activity), in contrast to に which would mark a destination for placement. たべる is written in hiragana rather than the more common kanji 食べる — a stylistic, slightly softer choice.