I would say that any hotel that has no more than a 5-minute walk outdoors from the arrival/departure passenger terminal buildings is more or less an on-site airport hotel for this purpose. Let's just say hotels where my relatives could use a stroller to get a child + luggage from the hotel to airline check-in without using any cars/shuttle vans/buses or any fare-due train/tram/bus.

Here are airports with something like such hotels:

ARN - Clarion + Radisson
BLL - Zleep
CPH - Clarion + Comfort
GOT -
SVG - Scandic
HEL - Scandic + Hilton + GLO
OSL - Park Inn + Radisson
CDG - Sheraton
AMS - Sheraton + Mercure
DUS - Sheraton
DEL - HEX
BGO - Clarion
SIN - Crowne Plaza
LHR - Sofitel, Hilton
LGW - Sofitel + Hampton + PI
MXP - Sheraton
MIA - MIAH
IAH - Marriott
MSP - IC
SCL - HI
DTW - Westin
ORD - Hilton
DEN - Westin
WAW - Courtyard + Renaissance
MUC - Hilton
DFW - Hyatt
MCT - Aerotel
YYZ - Sheraton