I would set expectations from recent prices before you fall in love with a house
If you are trying to figure out what a realistic budget looks like in Melville, NY, I would start with recent sold and pending pricing instead of online wishful thinking. The quick answer is that this market still asks buyers to be disciplined, because accepted pricing is leaving limited room for mistakes.
Over the previous 30 days, the typical sold price in Melville, NY was $1,250,000, while pending homes carried a typical asking price of $925,000 and active homes sat at $899,999. Recent offers landed at 98.8% of asking. That is a market where your payment comfort zone needs to be honest from day one.
I would read those numbers as a warning against shopping too far above your real ceiling. In a market with 1.94 months of supply and only 31 active listings, the wrong strategy is to chase homes at the top of your range and hope negotiation solves the gap.
Set your maximum monthly payment before you start comparing homes. Keep a separate cushion for closing costs, moving, and post-closing work so the purchase itself does not strain everything else. Focus your search on the range where you can compete cleanly and still breathe after closing.
