You wouldn't even have to have this along the entire route of I-35 along side downtown. It could just be over I-35 along side the lower end of downtown, particularly from the river to say 12th Street.
It would probably be necessary though to bury I-35 creating a tunnel. Then the elevated lanes of I-35 could be demolished. Then the top of the tunnel could be turned into a green roof with the park on top. You could also maybe have a single boulevard bisecting the park to connect East Austin to downtown. Either 6th Street or 7th Street would probably be where it would go, although, with the CapMetro red line on 4th Street, it might have to be there instead since the train would have to get across somehow.
If only I were a billionaire.
I hate that freeways are so utilitarian. They are necessary of course, but I wish they could be designed in a way that they contribute more to a city than just transportation. I've always thought the space above highways is wasted. I wouldn't suggest building skyscrapers on top of them, but creating a relaxing park on top of something that is hard, harsh and even cold (and hot) is an attractive idea.