$300 Electric Bill

Once a year ConEd goes into buildings and reads the meters.

If anyone's bill, based on estimated usage, is out of line with real usage, it's adjusted to meet the difference.
Were you a new tenant within the past 12 months ? If so, ConEd may be using the previous tenants usage from past years, and your usage is different.

When I lived in a 1BR floorthrough in a brownstone and ran two good-sized AC units in the summer I would get $300-400 electric bills. So, not unheard of.

But, electric power tools (saws particularly) can consume a fair amount of power. You might take the bill to the landlord and point out that this is an unusual bill, and you think they contractors have continued to use your power. Then ask the landlord to pay part of the bill (assuming they're constructing stuff for him).

Good luck.
The best way to "prove" this would probably involve comparison vs your previous summer months bills this summer and if you have been there more than 1 year, comparison to last summers as well.

$300 is not out of line at all for a 2BR AC'd in NYC...it could be worse!

I've easily run up a $400 AC summer bill my first summer in a couple apartment before realizing what the sweet spot is for thermostat comfort/cost in each place.

As Admin2009 pointed out - estimated bills can be a killer, check your bill to see if its an actual meter reading. I once had a $700 extra bill show up when they didn't read my meter for months and came back for the overage, though gave me 6-12 mo to pay it off.

My vote is on the use of the power saw by the workers outside your door. This happened to me when they were resurfacing the terraces in our building many years ago. I got a big electric bill and came home daily to the circuit breaker for the outside outlet tripped. Even when asked not to, the crews kept using the outlet, so in the end, I turned off the circuit breaker each morning before I went to work. That solved the problem.

And it's not going to solve your current problem, but I do recommend signing up for level billing if you've been in place for more than a year. (but that can also hide unusual spikes, if you're not vigilant).

Good luck