If it is exactly null (as opposed to not set):
db.states.find({"cities.name": null})
(but as javierfp points out, it also matches documents that have no cities array at all, I'm assuming that they do).
If it's the case that the property is not set:
db.states.find({"cities.name": {"$exists": false}})
I've tested the above with a collection created with these two inserts:
db.states.insert({"cities": [{name: "New York"}, {name: null}]})
db.states.insert({"cities": [{name: "Austin"}, {color: "blue"}]})
The first query finds the first state, the second query finds the second. If you want to find them both with one query you can make an $or query:
db.states.find({"$or": [
{"cities.name": null},
{"cities.name": {"$exists": false}}
]})