As soon as possible, depending on the place, it may not be vacant already. If you currently rent, I would check your lease to see provisions. Some leases allow you to get out of it early with no penalty (for example meaning you not still responsible to pay rent till June 30 even if you move out in April) if you give proper notice to the landlord.
Others epect you to pay no matter what. In that case, I would say start looking about 2 months before your have to move out.
What price range are you looking for? There are several rentals currently available with 2 or 3 bedrooms ranging from $1600 to $2300/month and most of them say immediate occupancy, (which in Edison is at least 10-14 days from lease signing due to the need for the township to inspect the home).
Give me a call or email me and I can send you what's available.