Betty's Bay is home to the Harold Porter Botanical Gardens which are worth exploring everyday of the week. (Literally, they are open 365 days a year!)
Take your student card for discounted entry and then in any weather the gardens are fun to roam. You can find out about the local fynbos (pronounced fain-bos) and native plants to the Western Cape. Grab a little energy filled lunch at the cute cafe and then head back to the entrance and ask for the key to Leopards Kloof.
Leopards Kloof is the valley up to the right if you are facing the gardens and is aptly named for the presence of leopards, although I have been several times and haven't ever seen one! Take a swimsuit and a pair of trainers for the fairly easy hike to the waterfall where although it does say you can't swim and it's freezing, it's irresistible.
The view is pretty irresistible too!