2-3 hours on the shinkansen from Tokyo would be best done as a round trip Tokyo - Nagoya on the Nozomi, about 1hr45 minutes each way. The Nozomi is the fastest shinkansen and after making one stop a few minutes out of Tokyo, typically doesn't stop next until Nagoya.

This ride will cost you each Y10,780 one way (i.e. double that for a round trip).

If you are content riding a Hikari, the next fastest shinkansen, which basically runs about as fast as the Nozomi on this sector, you could probably do a trip from Tokyo - Shizuoka and back, about 1 hr 10 minutes each way, for Y6180 each person each way. This could be done with either a 3 or 63 minute layover time in Shizuoka. Three minutes IS theoretically possible, but maybe best you go get a cup of coffee and go for the longer layover!