First, it is potentially dangerous to use 120vac mains directly. Switching power supply isolate their output with a feedback control that is opto isolated. If you do this at least use the neutral side of plug (larger width plug blade) for ground which only works for half wave rectifier. This won't help if you are using a full wave bridge as the neutral side reverses on each cycle.
Now, 120vac will give you 170 vac peak. With a full wave bridge you will get 120 vdc rms minus the 1.3-1.6 volt drop from two conducting rectifiers in the bridge.
An infinite value cap will charge to peak of sinewave, 170 vdc - 1.5vdc for rectifies. Full wave peaks occur at 120 Hz rate so there are 8.333 msec gap per peak.
Capacitor discharge is dependent on current discharged. Current from cap is I = C dV/dt where dV is drop in voltage over time period dt.
If you want to draw 10 amps with no more then 3 vdc of ripple drop from 168.5 volts then you would need a cap value of 10 amps * 8.333 msec / 3 volts = 27,800 uF. If you do this at half wave the time gap goes to 16.6 msec and the cap value has to double to last twice the discharge gap time.