We fly out of Islip all of the time!! Our favorite airport - so small, so close, so easy.
We live very close to the airport and always park in the MacArthur Airport economy lot and have not had problems finding a spot. The shuttle takes 2 minutes from your car to the terminal.
One caveat - Frontier airlines just started flying out of MacArthur a few weeks ago - I would assume that that will bring more cars into the lots. But, I anticipate that it will still be fairly easy to park.
You may want to look at taking the Bridgeport-Port Jefferson ferry to get from CT to NY - it is a little pricey, but it will save you the headache of the bridges. From Port Jefferson, it is an easy 20 minute ride to the airport.
https://www.88844ferry.com/SailingSchedule.aspx
I think the Hilton Garden Inn Islip/MacArthur Airport has stay and park. I would do your research on the reviews of the hotels in the immediate vicinity of the airport - a lot of them get very bad reviews, the Clarion being one of them.
I would put ISP back in the airports you include in your travel planning. We are flying on SW for a long weekend this month for $128 RT. You just have to keep watching the prices and I find that normally prices are lower out of Islip when there is not a big advertised SW fare sale. They are having to compete with Frontier airlines now.