Is there an easy way for me to determine how much less of my tax money is withheld for each allowance taken?

You would have to discuss with your payroll person. It isn't possible to determine unless you give all the relevent information which you shouldn't do over the internet. Your payroll manager should be able to provide input on this matter or perhaps an HR Block type establishment.

I think the withholding tables are published in Circular E (an IRS pub). They change each year.