I'll let others speak as to driving time for LGA/JFK, but have you considered flying into/out if HPN (Westchester County Airport) -- It is served by AA via American Eagle through ORD. (I am assuming you are an AA flyer, based on the info under your handle.) I'd say you are 20-40 minutes away from Fishkill.
If you are truly flexible, also look at SWF (Newburgh/Stewart Airport), while on the other side of the Hudson, you are 15 minutes or less from Fishkill. -- Currently only has US Service via PHL, and DL via DTW/ATL.
Id say by choosing HPN/SWF you are looking at at least 30-60 minutes savings in drive time each way, maybe more. Both airports are small, rarely have awful security lines (SWF usually has but one or two people ahead if you), and are served by most major car companies. The downside would be the requirEd connection, but well worth it, if you ask me.