For several months I have had banging in my pipes. First happened in maybe March? Was terrible, at random times until we changed the fill valve in the toilet nearest the noise. About a month later we had pipe burst on our side of the water meter. We had a plumber make repairs, and he also installed a pressure regulator, as our fill valves seemed to last next to no time. Problem solved for about a month. Then the banging resumed whenever the downstairs toilet was flushed. Not during flushing, but during the filling of the tank. We turned up the water pressure a bit, and that helped for about a day. The banging came back. We tried draining and flushing the hot water tank. Did not help. We drained the entire water system, thinking that maybe the air chambers had been flooded by the previous high pressure. Did not help. Now we are hearing the banging whenever the washing machine fills, when any toilet is refilling, and when we take a shower. What could be causing this? Our pressure is now just below 60.

lower it to 45, see what happens.
when the pressure regulator was installed, was an expansion tank installed also?

I'm not sure, but I don't think an expansion tank was installed. Would it be in the same location, and what would it look like?

generally an expansion tank is installed in the cold water supply to the water heater.
looks like this...

when the water heater turns on it will cause the water to expand in size thus creating more pressure.

Definitely no expansion tank. Will attempt to lower pressure. Any other thoughts?

get a gauge that screws onto a hose valve. get the type that has a lazy hand. attach it and leave it all night to see if the pressure spikes.
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If you can easily get the noise started, go around listening and feeling the cold water pipe and try and find where the noise is originating from. Start at the main shut off valve.

When water pipes run up and then down it creates an area for air to be trapped in the pipe causing a vapor lock type condition. The air is trying to go up against the water flow resulting in the banging. Locating the high point and installing an automatic air bleed valve @ the high point should eliminate the problem. If that isn't possible due to construction restraints you could try creating a pre high point where you install the air bleeder to remove the air before it feeds out to the rest of the system. This type of problem is usually not in the potable hot water side of the system but is common in a closed loop hot water home heating system such as baseboards.

Turned the water pressure down to 45. So far so good...