I assume that the "new" alternator is a dual feed alternator, which will require you to ground one terminal in order to use it with a stock type voltage regulator or the one that I sell (link below). I sell a solid state voltage regulator that would be a direct bolt in for the stock '68 style voltage regulator currently in your car.
On the '70 & up MOPARS with the three wire voltage regulator they were mounted near the wiper motor on the upper portion of the firewall. They should be away from direct engine heat.
The stock alternator for your '68 Chrysler was likely a 37 amp unit unless you had A/C or a heavy duty charging system in which case the alternator would be around 45 amps.
If you are going to use a 60 amp or higher alternator I STRONGLY recommend that you upgrade the wiring in the charging circuit and bypass the alternator gauge in the dash to avoid an electrical fire.
The '70 & up style voltage regulator is a great unit if you get a quality part but if you want a stock appearance you would need to hide it somewhere away from direct heat.
Mopar Voltage Regulator - Electronic Solid State with Correct Restoration Look | eBay