“Romantic” paddling spots around Austin?

My girlfriend and I are going to be in Austin for a couple days. Any ideas on where to go for an awesome flat water day trip? Hoping for something a little extra like a secluded picnic spot, perfect sunset or any other suggestions. Thanks in advance!

It’s been many years, but the Perdenalis River was beautiful. I hiked and camped near it but that was before I started paddling so I can’t speak to that.

Austin, TX? Does flat water include flat water rivers? Do you need to rent?