Follow the River Torrens from city to beach, checking out all the native bird life along the way!
You can hire a free bike from several locations in Adelaide (https://www.bikesa.asn.au/adelaidefreebikes).
Closer to the beach there are horses you can stop to pat, and then when you get to the end of the trail, turn right to grab a coffee (I recommend Malobo).
The trail is about 15km each way (sounds daunting, but it's a fairly flat ride). Join the trail anywhere along the Torrens river (it runs on both sides from the city, and then just from the northern side after the Parklands).