3. MLS listings through a Realtor.
By southern part of New Trier district I assume you're thinking of Wilmette. You can also drive around neighborhoods that interest you and look for FOR RENT signs. They're out there.
A Realtor can be a great help and, in the Chicago area, the landlord pays the broker fee. That's not the case in other parts of the country.
No, you are not stuck looking for rentals on Craistlist. You can call a local Realtor. We are able to search for rentals by school district from our MLS. The agent will be able to provide you with interior photos, length of lease, if pets are allowed, etc..
I hope this helps!