B737-700
Flight Crew Last 90 Days 241
Situational Awareness
Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Flight Crew Became Reoriented
Human Factors
We were descending on the MIP4 Arrival into LGA. We were cleared to the BILEY intersection at 13;000 feet and were then re-cleared to cross [BEUTY] intersection at 10;000 feet.  On the descent to cross [BEUTY] intersection at 10;000 feet; ATC queried us if we would make the restriction. It was at this point that we realized we'd put [another airport] altimeter setting of 29.52 instead of LGA's setting of 30.52 into our altimeter. We fixed it and made the 10;000 foot restriction. We are unsure if we missed the BILEY at 13;000 foot restriction; but the Captain stated we were cleared to [the] intersection to cross at 10;000 feet BEFORE reaching BILEY at 13;000 feet. Otherwise we missed the BILEY at 13;000 foot restriction; but I'm not sure.We just missed the check in multiple spots.  The Approach Checklist should have caught it but we saw the [old] altimeter setting that happened to be exactly 1;000 foot difference on altimeter.
I usually do a much more thorough review of ATIS information checking the weather sheet against ACARS. Not that it is an excuse but we anticipated an hourly weather report before approach; and I believe I did not do as thorough of a review of the previous weather.
A B737-700 flight crew reported they had incorrectly set the altimeter by an inch of mercury while on arrival into LGA.