Lately we have been broiling vegetables in the oven with a little bit of extra virgin olive oil on them, but we keep setting off the smoke alarm in the kitchen although the vegetables come out deliciously. What oil has a high enough smoking temperature to be appropriate?
If you like the taste but not the fire alarm, either turn on your hood/vent or disconnect the fire alarm while cooking. If the flavor isn't burned, changing the oil will likely change the flavor as olive oil has a distinct flavor that is missing in other oils.
If this isn't a solution for you, choose any neutral, high smoke point oil you like. Canola is popular choice for most vegetables. It has little flavor and a decently high, 400°F/205°C, smoke point, somewhat higher than olive oil's 325-375°F/165-190°C.
For a really high smoke point, try safflower (510°F/265°C), or even light olive oil (465°F/240°C), though you may have the slightly lower soybean or peanut oils (450°F/230°C) in your kitchen already. The chart lists peanut as "neutral" but I tend to feel it has a flavor and it has the added issue of being a no-go for people with peanut allergies.
If you have the time, you might also consider clarified butter (450°F/230°C), which should be delicious with vegetables.