Answer: 1 mole of stacked pennies would reach a height of 5.69x10^17 miles.
Explanation: The U.S. penny has a thinkness of 1.52mm. One mole of pennies would have:
(1 mole pennies)(6.02x10^23 pennies/mole)*(1.52mm/penny) = 9.15x10^23 mm for 1 mole of pennies. One mile = 1.609x10^6 mm.
(9.15x10^23 mm)/( 1.609x10^6 mm/mile) = 5.69x10^17 miles for 1 mole of pennies.
That would reach Alpha Centauri (5.69x10^17 miles/2.6 x 10^13 miles)= 2.19x10^4 times.
There is a coin shortage in the US, so good luck. Send me your spare pennies.
[Note: I did this quickly, so please check the work. A mole is indeed a big number, but . . .]