I Recently Purchased An Older Home And The Water Pressure Is Very Low At All The Faucets. I Have "city" Water Not A Well. The House Was Unlived In For Almost A Year, Could This Be Part Of My Problem?

Remove all areators and clean but do not reinstall yet. Flush the water heater with the main in the on posotion. Does any improvement happen? You can have all sortd of trash and debris in your lines so flushing out the whole house is needed. If you have stops under the sinks the stops may have to be opened and the ports inspected. Does you outside spigot appear to have good pressure/volume.

How old is old? You may have a lead water service. Try everything that ballengerb suggested first. If that doesn't work. Look for galv fittings near your incoming water. If all of your faucets have poor pressure, your problem is most likely somewhere in your main water supply. You should be able to ask your city water department what kind of water service you have. If its lead, I feel for you. I have a lead service and opted to install a grunfos on demand pump instead of tearing up my yard to replace my water supply. It is only a temporary fix though. If you have lead under ground, sooner or later you will have a leak underground.

Follow Bob's instructions I am adding this just to say how to flush your water heater, and also check the water pressure with a pressure test gauge, see the (Image) below.

If your water heater is gas, set the gas valve to "Pilot" to prevent the burners from coming on while you are flushing it. If your heater is electric be sure to turn off the circuit breakers. With an electric water heater, if the water level drops below the heating elements and the thermostat turns the elements on, the heating elements will probably burn out quite rapidly.
Connect a garden hose to the drain valve at the bottom of the tank. Make sure the outlet of the hose is in a safe area away from pets and children. It can be very hot and can scald quickly

Open the drain valve at the bottom of the heater allowing the water to flow out through the garden hose.

When the garden hose runs clear you are finished, good luck.

John