AW S1 requires the iPhone for GPS map.
AW S2-S3-S4 does not require the phone.
Word of warning - although the AW S1 requires the phone, that does not mean the software will support it. So check with your app of choice. Default Apple Workout App does support it. However, Nike Run Club will not draw a map on a S1 when you take your phone. It used to, but they removed that feature a year or so back.