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Another one of the iconic, coveted neighborhoods comprising the famous 78704 south Austin zip code is Travis Heights, nestled between S. Congress and I-35 just south of the river. Travis Heights homes combine an eclectic mix of styles and a quiet, secluded feel despite their close proximity to lively South Congress. If you're looking for a trendy neighborhood with quick-access to some of Austin's hottest shops, restaurants and bars, then Travis Heights has it all.