The cafe is South Beach Kiosk, which is currently open from 9am to 6pm. South Beach Reserve is also on the free CAT bus route and has a cycle path running through it, so there's no need to drive. Anytime is a good time for a picnic here, but around early evening when the sun is setting can be spectacular.
John Tonkin Reserve is on the banks of the Swan River in East Fremantle, you may be lucky enough to see dolphins if you picnic here. It has all the facilities mentioned above. The cafe, Zephyr, is open from 7.30am to 4pm.
You may be lucky enough to see dolphins at John Tonkin Reserve