Looking for all day parking recommendations near Hermann Park

We are relatively new to Houston and planning to visit the Japanese Garden and Museum of Natural Sciences tomorrow. I have read tons of horror stories about parking over there on the weekend and based on my brief research, I could park at (1) 6400 Fannin St. Parking garage or (2) Fannin South Transit Center and take the rail. Are there any other options that would be better for us or do we go ahead with one of these?