Zilker Botanical Garden is one of the best things to do for free in Austin, and it's a fantastic date spot. Take your sweetie to the little tea house in the Japanese Garden area to look out and see the city. Stroll through the bamboo forest, which although graffitied, is still lovely. The waterfall is beautiful, and a great spot for a photo op. Be sure to come by when the roses are in bloom, as it's a wonderful sight. This is a instant stress reliever for me, and it's usually very peaceful here.