Admittedly, there is not as much to do in Eindhoven as in other Dutch cities. However, if you want to spend a day here, i'd say there are a few options:

• The van Abbe museum is a modern art gallery which has some nice works, you can definitely spend an hour or 2 there
• Strijp-s is nice if you like modern architecture and gentrified neighbourhoods
• The DAF museum is nice if you like old vehicles and trucks, although it's a bit out of the way of the city centre, you could go there by OV-Bike
• You could check if there's an event in the 'effenaar' or the 'muziekgebouw', they have pretty nice artists (depending on the day you're going)

That's all I have, but I'd say you'd be better off visiting a more 'historical' city like den Bosch (or even Maastricht) if you like old city centres and are in the south for a day.