I'm not sure if they are open in the winter, but a GREAT hidden spot is a city park on Lake Austin. Emma Long Metropolitan Park
Emma Long Metropolitan Park | AustinTexas.gov $25/night
Other spots
https://www.outdoorsy.com/rv-parks-a...unds/austin-tx
www.campspot.com may have spots for $27-30/night near Lake Travis
Next if you are okay with a 30-40 drive to your brother, check in Marble Falls, then Burnet.
South Austin area
Check for tiny home lots off South Congress near Slaughter Ln if they are still there.
If the farms and ranches haven't been developed in Buda, check that area. Also Dripping Springs outskirts...