Shinkasen train from Kobe?

I have looked on the Hyperdia website and cannot see any Shinkasen trains leaving Kobe to Tokyo. It appears that one has to take a local train to Osaka and then the bullet train to Tokyo. Is this correct? We are disembarking on March 26th in Kobe. What is the best or fastest route to Tokyo (Marounichi district)? We really wanted to take the Shinkasen.

Shinkansen trains depart from Shinkobe station, which is a short subway ride from the city center.

Check out this page here:

http://www.japan-guide.com/e/e3554.html

There are schedule revisions on JR Lines throughout Japan, including Tokaido Shinkansen on 15th March. As a result, hyperdia have yet to show correct train connections at all for your trip for the moment.

The new Tokyo-bound departures at Shin-Kobe in the daytime are as follows:
Nozomi: 02, 22 and 46 past the hour (about 2 hours 50 minutes to Tokyo)
Hikari: 25 past the hour (about 3 hours 15 minutes to Tokyo)

You seems to be leaning toward the bullet train so that the following advice may sound futile, but Skymark Airlines now sell a 7,000yen ticket from Kobe to Tokyo Haneda each way for that particular day. Flight time is only 1 hour and there are 8 flights a day. Worth considering.

the problem with flights of a short duration is that one has to go to the airport then wait to register then go thru security etc. often a 1hr flight turn out to be nearly 3 hrs downtown to downtown. when in Kobe I usually stay by Sannomiya station. it takes me 10 minutes by subway to go to Shin Kobe and if I time it right (by reserving the train seat in advance etc.) I can be on my way 10 minutes later maximum.
London to Paris is now faster by the Eurostar than by plane, again from downtown to downtown.

I failed to put the airline's link:
http://www.skymark.co.jp/en/index.html

@Sensei
I just gave the airline info to let OP know that a very cheap fare is now available on that segment for the day OP is traveling. Skymark's normal price from Kobe to Haneda is 11,000yen (of course OP could snatch the 7,000yen ticket now if OP should change his or her mind), while the Shinkansen's 14,870yen on a Nozomi reserved seat.

I'd show a time comparison.

1) From Sannomiya to Tokyo by Shinkansen Nozomi:
Sannomiya 10:23--Subway (200yen)--10:26 Shinkobe 10:46--Nozomi12 (14,870yen)--13:33 Tokyo
Total duration; 3 hours 10 minutes
Total cost; 15,070yen

2) By Air
Sannomiya 10:20--Portliner (320yen)--10:38 Kobe Airport 11:20--SKY106 (11,000yen)--12:30 Haneda Terminal 1 13:01--Monorail (470yen)--13:17 Hamamatsucho 13:23--Keihintohoku Line (150yen)--13:28 Tokyo
Total duration; 3 hours 8 minutes
Total cost; 11,940yen, or 7,940yen if the bargain price ticket could be obtained.

As you have pointed out, total duration of both means is nearly equal. But what I wanted to indicate in the previous post was that the price difference between Shinkansen and flight couldn't be overlooked.

O.K., you make a very good point for a plane after considering the comparative costs. Now . . considering that my husband and I will be coming off a ship and will each have a carryon and one 26" rolling bag, which means of transportation is less burdensome? Also, we will be staying at the Palace Hotel in the Maranouchi area. I suppose a cab from the monorail to the hotel would be easier, albeit more expensive.

Taking the Shinkansen with one connection in ShinKobe looks to be the less burdensome option.

Flying is a hassle, not to mention it requires you to take more transfers and go through all the airline procedures.

Whether you take the Shinkansen or fly, traveling with the rolling bag would be cumbersome.

If the train is busy, you'll wonder what to do with it, and Skymark imposes an excess baggage charge in case check in luggage is beyond 15kg.

There seems to be a courier, or what is called 'Takkyubin' counter in Kobe Port Terminal. You might consider depisiting your bag there upon disembarkation and have it delivered to your hotel in Tokyo the next day. It's less than 2,000yen per piece.
http://www.japan-guide.com/e/e2278.html

Refer to Skymark's article 36 on their excess baggage policy.
http://www.skymark.co.jp/en/conditions.html

Shinkansen trip could be an experience if you have never taken it before, though a domestic flight won't be so complicated as an international one. Skymark's check in closure is 20 minutes before departure. It's up to you which to choose.

Have a nice trip.

What a great idea, Optimistk! That will take care of the problem; and, yes, we do want to experience a Shinkansen.