"Where should we go for dinner?"
I haven’t seen dao used this way before.
What is the difference between the use of dao versus zai in this sentence?
Trying to imagine the nuance: Is it sort of a ‘where should we end up for dinner tonight?’ versus ‘where exactly will we go?’
Or is it a set phrase?
i think the "should" threw me off, but shouldn't "我们应该去哪里吃晚饭" also be accepted?
应该 is used as a suggestion to other people, e.g. 你不应该熬夜 (you shouldn't stay up late). In the case of this example, 我们应该去哪儿吃晚饭, the 应该 wouldn't really make sense. The "should" is already included in the sentence 我们去哪儿吃晚饭 as the 我们 indicates that it's a question to "us" :-)
The "should" adds unnecessary complication. 到哪儿 simply means "go where?" as in 你到哪儿 - where are you going?