I have a 1988 Corvette 35th Anniversary Edition with 3,900 mile on it. It runs very well and is overall in showroom condition. Just this week the digital oil gauge began reading between 60 and 70 lbs of pressure at idle and drops slightly on a short drive. Is this something I need to be concerned about? No warning lights have come on. Can anyone explain and let me know if I need to address this situation?

You say this just started? What was the oil pressure readings before? 60-70 psi is nothing to worry about if it is correct, but if the "normal" pressure before was lower, like 30- 40 psi or so, then your sending unit is probably on it's way out.
 The wiring from the sender may also be shorting out somewhere, most likely in the engine compartment. Not sure where the sender unit is on the '88, but it could be either down by the oil filter, or it may be right next to the distributor, on the driver side.

Thanks very much. It was 30-40 lbs and went 60-70 lbs recently. I will check the wiring and replace the sending unit if needed. It is the oil pressure gage sensor correct? Looks uncomplicated to remove and replace. Is that true?

It's not to hard to replace, especially if yours is down by the oil filter...just a simple unscrew/replace deal.
If yours is up by the distributor, it's a tight fit up in there, so patience is a big help! Also, there is an oil pressure sender for the fuel pump by the distributor, so be sure you are replacing the correct unit, if there are two in that location.