OK - didn't see the first part of your question. A bit interesting to ask 'without flying' on an aviation message board, but I will outline your choices below:
Basically two options are available to you - Shinkansen (bullet train) or limited express sleeper train. If you have a JR
Rail Pass, you will have to pay extra for a berth on a sleeper train (that is not included in the pass). If you take Shinkansen, that service is included in the JR
Rail Pass, and you can transfer to a regular limited express train for a day trip.
If you take Shinkansen (bullet train):
1. Take the Joetsu Shinkansen "Toki" or "Max-Toki" from Niigata to Tokyo. This will take you about 2.5 hours.
2. From Tokyo Station, take the Tohoku Shinkansen "Hayate" to Hachinohe Station. This will take about 4 hours.
3. Take the Limited Express "Super Hakucho" from Hachinohe Station to Hakodate Station. This will take about 3 hours.
If you want to take a sleeper train, you can do it this way:
1. Take the Joetsu Shinkansen to Ueno Station (station before Tokyo Station). About 2.5 hours.
2. Take the Limited Express sleeper train "Cassiopeia" or "Hokutosei" from Ueno Station to Hakodate Station (these trains end in Sapporo). You will leave around 16:00 in the afternoon and arrive in Hakodate around 4:00-6:00 in the morning, depending on the train.
From Sapporo, you can choose between the sleeper train listed above, or if you choose to travel during the day:
1. Take a Limited Express train from Sapporo to Hakodate.
2. Take the Limited Express train "Super Hakucho" from Hakodate to Hachinohe.
3. Take the Tohoku Shinkansen "Hayate" from Hachinohe to Tokyo.
To go to Narita Airport, you can take the JR
Narita Express from Tokyo to Narita Airport. As Narita Airport has two stations: Airport Terminal 2 and Narita Airport (Terminal 1), check with your airline to find out which station you have to use.
If you can read Japanese, you can check out the JR
East electronic timetable and find out the schedule of different train lines here. NOTE - this is for JR
East services only (Eastern Honshu), but other JR
companies may have similar resources for their service areas.
Hope this helps you.