Define 'northwest' city/ town names will help.
There is a nice state park in the city of Austin - McKinney Falls SP - 50Amp/W - $24 per night, 30Amp/W - $20 per night. No FHU sites - there is a $6 per person, per day entrance fee if you do not purchase a $70 Texas State Parks annual pass.
Traffic within the city of Austin if horrible for RVs - especially during the morning and evening rush hours (6-10 am / 3-7 pm). I try to time my drives through town between 10 and 2 on I-35, otherwise I take US-281 west of town or US-77 east of town to avoid the hassle.
Lake Georgetown and Granger Lake each have two COE parks. They are north of Austin about 30 miles. The parks are nice. W/E only - no FHU sites.
Lake Georgetown is currently almost 11 feet below conservation stage. Much of Texas has been in a drought recently, but our lakes are suffering more for over usage. Substantial new home building and population growth has out run the available water supply in many areas - Austin - especially north of the city - is one area with major issues. Even with a near normal rainfall year the lakes are not able to recover.
West and northwest of Austin near Hwy 281 are several nice locations - our personal favorite is Inks Lake SP west of Burnett.
Full-Time 2014 - ????
โNot all who wander are lost.โ
"You were supposed to turn back at the last street."
2012 Ram 2500 Mega Cab
2014 Flagstaff 832IKBS TT