I don’t stay at SYD airport hotels (living < 20 min drive away) but I was surprised just how many there are now, especially over the domestic terminal. I did a morning T1 dropoff earlier in the week, my GPS suggested an alternate route home to bypass morning peak traffic and took me past the Pullman and surrounding hotels.
That side is relatively close to Mascot train station, so easy access to the city if you have time as well train to/from Dom T2/3 or Int T1.
BTW, before you decide to walk from T2/3, check the next 350 bus. It departs from right outside QF arrivals and goes past the Pullman and HIE etc before heading east on a very circuitous route to Maroubra, Coogee and after an hour or so, Bondi Junction (I have a stop around the corner but pass on that one! Although I imagine backpackers love it).