Usually the jurisdiction where the incident occurred is where the action is filed, and then any parties that want to request a change of venue for whatever reason would need to petition for it.
Keep in mind that generally speaking, the statute of limitations for filing small-claims actions is one year from the date of the incident, unless extenuating circumstances or reasonable evidence to show due diligence at exhausting other avenues first (in a reasonably timely manner) exist.
Edit (sorry I forgot to address one of your questions): It could go either way; I would suggest going after the neighbor who initially agreed to pay for the repairs, who will likely raise the defense that it's the landlord's responsibility (at which point you should ask them to show how/when/etc. they notified the landlord of the defect). If they can show that the landlord was reasonably aware of the defect, and that their own negligence or misuse/abuse didn't cause the faulty window to fall out, then you will likely need to sue the landlord instead.

