Well, it would depends on what you want to do. Just riding the Shinkansen for the purpose of riding the Shinkansen I think is a somewhat waste of money. I personally would combine it with a trip somewhere as part of my travel plans, or at least try to incorporate it.

You say you are in Tokyo for 1 1/2 days will you be traveling anywhere else in Japan after Tokyo, or is this a short layover?

I would if you don't want to spend a fortune is to take the Shinkansen from Tokyo Station to Odawara Station (about 35 minute ride). Get out at Odawara visit Odarawa Castle. Or if you have a full day from Odawara Station you can explore Hakone.

Most trains that stop at Odawara Station are "Kodama Shinkansen" services, these are the "slowest" of the Tokaido Shinkansen services, however they are much faster than regular trains taking 35minutes vs. 1.5-2hrs from Central Tokyo by regular trains, and they are Series 300 Shinkansen trains.