Don't forget to get tea before you leave. It beautifully rounds out the whole experience. If you have the time, I'd recommend sitting at one of the many benches to enjoy the scenery. Try taking in every boulders, every plant delicately springing from each crevice. You'll be surprised how much detail your eyes can gloss over by just taking a picture and moving on.
I had always heard that this was a cool place to visit, and I'd agree. You can take your time and probably be there for several hours, or you can "quickly" walk through all gardens and exhibits. There are free tours, which we started, but the group was too large to make it worth it. You learn A LOT of information on the guided tour (maybe not all of it will interest you, but some of the fun facts would). Great introduction to Japanese culture.