The basal metabolic rate is the baseline energy turnover of a person who is awake but completely at rest, kept in a thermoneutral room, and fasted long enough (roughly 12 hours) that digestion and absorption no longer add to metabolism. Two of the listed choices are ruled out immediately by this definition: daily activity and food intake both raise metabolism above the basal floor, so neither can be the variable BMR is anchored to.
That leaves body surface area versus lean body mass. Historically BMR was reported per square metre of surface area because heat loss tracks surface area, and this made comparisons between individuals convenient. However, the tissue that actually burns the fuel is the fat-free (lean) tissue; fat stores contribute very little resting metabolism.
A simple thought experiment settles it: take two individuals with identical surface area. The one with more muscle and less fat (greater lean mass) consistently shows a higher basal rate, because the allometric relationship $\text{BMR} \propto \text{weight}^{0.75}$ reflects metabolically active mass. Thus lean body mass is the single factor BMR correlates with most tightly.
\[\boxed{\text{Lean body mass}}\]