Regenerative braking, without a battery?

Have you determined the exact amount of energy you're going to need to store? The single hardest part is going to be the alternator and calculated resistance of the load device you're going to need. The series resistance of power caps especially at DC loads varies pretty dramatically from maker to maker and model to model, and most are in the range of -20 to +80% variation on the capacitance value and series resistances are all over the place and are a key factor in designing something that will absorb the energy in a controlled manner, a capacitor is only going to provide a fixed load with a lot of variability over operating conditions that may not be long term predictable. I'd start with working out how much energy in joules it takes to start/stop the mass over a safe time frame and work out from there before you go picking devices. The motor is going to be a real problem. I think the Army is currently working with rotating case motors (commonly called outrunners) that are the size of the entire wheel as that's the only practical way of producing enough torque/efficiency in a bike style wheel, the mechanical construction of a motor attachment to the power train is going to be the real design problem, as I'm guessing you don't have the ability to design and build a custom outrunner the size of a bike wheel; Power storage will be almost irrelevant compared to that as far as effectiveness go.