What's the inductor for? You have an excellent voltage regulator and decoupling capacitors.
Inductors are used before a regulator and its input cap but after the main smoothing cap if the supply to it has wild voltage fluctuations. If you are using a little 9V battery then its voltage won't swing wildly and an inductor isn't necessary.
A 7805 needs an input voltage of about 7V to 8V and won't work when the 9V battery's voltage runs down to 6V during its life. I use an LM2931AZ 5.0 low-dropout regulator for all my 9V battery applications because it still regulates with an input voltage of only 5.4V.
The only place I've seen them used is before the regulator, but ONLY on switch-mode PSU's - on a conventional PSU or a battery, the value is FAR too low to do anything.