Bern Botanical Garden

I was there a few years ago. It's not huge...Maybe an hour, hour and a half if you stop to sit in the garden or cafe. Possibly longer if you go into all the buildings (Palm house, orchids etc) and really want to look closely at each and every plant.
Very pleasant to visit on a warm day and there is a nice little cafe too. If you walk from the top (bridge entrance) down, you can end on the riverside path which you can then follow all the way to the Bear Park area.

Edited just to clarify that I agree with Maureen that it's not worth a special trip out of your way like Kew Gardens in London or anything, but I didn't want to discourage you from doing something different and following your own interests. I always check out the local bookstore when I visit places and can sometimes spend hours at museums or castle ruins that other people find dull and skippable - so you never know what people will find interesting! Anyway, it is by no means a 'must-see,' but it's free and a nice place to get away from the hustle and bustle, just enjoy a quiet moment and then combine with a walk along the river. And I'll add a second vote for visiting the Rose Garden as well!

thank you!

I'm another fan of the Rose Garden, and its bench with the statue.