Recommendation Needed for Apartment/Townhouse Rental

Hi everyone! My husband and I are moving from the DFW area to Austin with our two dogs and would love some housing recommendations.

Budget: $2000 per month
Location: No preference. Open to both city and Suburbs
Wishlist: Safe area with low crime rate
Proximity to daily stores and grocery essentials
Yard for the doggies

We are just starting our research, so any specific neighborhood recommendations, suburb suggestions (like Cedar Park, Georgetown, Round Rock, Buda, etc.), or even specific property management companies that fit this vibe would be incredibly helpful.

TIA