Hello Rosie,
It is certainly possible to use the JR Pass for travel between HFukuoka (JR Hakata) and Ueno.
Here is am example route I looked up for you.
You can also use Hyperdia to look up route information yourself. To do so, click below the search bars on SearchDetails and de-select Airplane, Airport Shuttle Bus, NOZOMI / MIZUHO / HAYABUSA (SHINKANSEN), Private Railway. This way you know that the route is always covered by the JR Pass.
One thing to note: You can leave the Nozimi / Muzuho/Hayabusa select if you travel north of Tokyo on the Tohoku Shinkansen as the Hayabusa train is covered by the JR Pass.
For more details: see our blog post on how to plan using Hyperdia.
The Shinkansen between Fukuoka - Tokyo basically is one long train line with many interesting stops along the way. Think about Hiroshima, Himeji, Kobe, Osaka, Kyoto, Shizuoka, Nagoya, Hakone (Odawara) and more. So there are a lot of good places to make a stop at. Have a look at this Map and I am sure that you get the idea.
Hope this helps,
Daniel