Less than 2km north from the city centre, the Royal Botanic Garden is worth a visit no matter the season. Entry to the large beautiful gardens is free, but you should not miss visiting the magnificent glasshouses with 10 different climatic zones and over 3000 exotic plants.
During the Spring and Summer months, Daily Garden walks with a guide start at 11:00 and 14:00 (additional charge) from the John Hope Gateway reception and are a great way to discover the seasonal highlights and hidden treasures. 
There are many other regular events for young and old, check the website for details