Amy's casita is perfect for medium-length walks to the Capitol building (passing Franklin BBQ on the way to/from), and even shorter walks to many great cafes and restaurants. If you're younger and want to hit the 6th Avenue weekend zoo, you can actually avoid all the parking issues (and noise) by staying here and walking or taking Uber/Lyfter.
Rockstar Bagels is about a 3-5 minute walk and Figure 8 coffee another 3-5, so if you need a quick breakfast, they're both very close. Try Flyrite for excellent chicken sandwiches (short drive/~20 minute walk), and Prohibition Dairy for Boozy Shakes and great-interesting ice cream flavors. Republic Donuts ... super friendly owner, interesting choices, and limited times that they're open. Be sure to stop to see the mini-museum in the Texas State Cemetary on the way to or from these various shops.
This is a QUIET area, we felt like we were removed from all the city noise, while still being close to everything.