What to do in Bern in half a day (tomorrow afternoon)?

Hi people,

I just had an unexpected offer of a Basel-Bern-Basel ticket - valid until tomorrow, the buyer can not use it and probably not refundable any more.

I never been to Bern so I thought why not. But I have no idea what to do and not much time to research it.
Any sightseeing suggestions?
I'm also open for suggestions that don't take me all the way to Bern, as long as the ticket is valid.

I think to carry a bicycle on the train you have to pay a separate ticket. From reading the wikitravel guide, I believe there are/were free bikes to "rent" for 4 hours (with a deposit of 20 CHF) - anyone know more? Otherwise I can take a kick scooter with me to, well, scoot around.