I bought my Osprey Talon 33 to serve the exact same multi-purposes you mention. I LOVE it.
It is the perfect size for groceries, hugs your back while biking (in fact I chose it from a review website for mountain bike packs), and for weekend backpacking trips it can even hold a bear can.
Have run with it. It's larger than what I need/use for a 4-12 hour adventure race. Always awkward to run with a pack this big (33 liters) no matter how well made, IMO. At least it compresses and hugs the back well. Have run to the grocery store and walked back. If you do a lot of running/adventure racing, might want to go with a ~22 liter size - but then it won't be big enough to do a backpacking trip with. I also think 22L wouldn't be nearly enough space for a usual grocery trip.
I did cut off about 6 oz. of unneeded loops, straps, etc. to lighten it up.