About a 10 minute walk uphill from the International Rose Test Garden is the Japanese Gardens.   There's an entry fee (less than $10).  The garden doesn't take up that much space - it's fairly compact.  It took us less than an hour to wander around.  Of course, we had just come back from Asia, where we saw a similar style of gardens that put these gardens to shame.  There's lots of photo ops, with streams, a koi pond, bamboo, sand gardens, and traditionally styled buildings.  Part of the garden is wheelchair accessible.