Two Days In Basel

I am going to spend two days in Basel with my fiancé at the beginning of June.
What's not to miss?
We already know we want to visit Fondation Beyeler, but, apart from that, we are open to any kind of suggestions.
Any help will be appreciated, thanks.

The Tinguely Museum was the highlight of my visit. The Townhall and the Cathedral were nice. I also enjoyed walking along the river promenade and the old town, with a lot of quaint streets and buildings which are not marked on any guidebook. Still a guidebook would tell you more than you can find here.

Thank you so much for your reply.
I am also looking for suggestions about cafès (especially places where we can have a nice, reasonably priced breakfast, as the hotel we are staying at offers a terribly overpriced one) and interesting shops, if you have any.

hi emmalic, cannot comment on your further questions, however if you're interested in either art or architecture, apart from the Beyeler there's a couple of other places one could suggest:
- the Vitra Design Museum (just a short distance across the border from the Beyeler in Weil), which apart from its collection offers a selection of fine contemporary architecture from different architecs
- the Schaulager is just as well an interesting bulding (by Herzog/de Meuron) as a very special exhibition space, it's located a bit on the outskirts, though

further, are you aware that it's possible (and popular) to take a swim downstream in the Rhine? bring your swimming things, though on a second thought in June it still might be too fresh...

regards

Thank you Nautiker.
I would love to visit the Vitra Design Museum, but I am afraid we won't be able to make it fit in our short trip.
Oh well, next time!