I can't give you the exchange rates after independence was declared, but I can give you the exchange rates a year earlier - 1775. Luckily, John McCusker has combed through thousands of references and transactions to find out what the various currencies in use in colonial America were valued at. The best resource, for your question, is his 1992 book Money and Exchange in Europe and America, 1600-1775: A Handbook.

There were at least 17 different currencies in circulation in the British Colonies in 1775 - Massachusetts, New York, New Jersey, Pennsylvania, Maryland, Virginia, North Carolina, South Carolina, Georgia, Barbados, Jamaica, Antigua, St. Christopher, Nevis, Grenada, Bermuda, and Nova Scotia (Halifax). After declaring independence there would be the Continental currency as well. Connecticut, Rhode Island, and New Hampshire also had their own currencies, but the values were largely the same as the Massachusetts currency.

Below is a table showing the value of each currency compared to £100 sterling on the London exchange.

Colony	Value (£)
London	100.00
Massachusetts	117.45
New York	171.55
New Jersey	169.50
Pennsylvania	161.12
Maryland (1)	156.68
Virginia	120.00
North Carolina	175.00
South Carolina	758.67
Georgia	108.00
Barbados	140.00
Jamaica	140.00
Antigua	176.25
St. Christopher (2)	165.00
Nevis	175.03
Grenada (3)	160.00
Bermuda (4)	147.50

(1) Maryland conversion for hard currency. Paper currency exchange was 133.33

(2) Value for 1770

(3) Value for 1772

(4) Value for 1770

(5) Not enough data for Nova Scotia