After doing a lot of schedule research for a trip last year, I agree with Rick's guidebook recommendation to stay in Flam or Aurland if you have just one night to spend along the Nutshell route and no car. Actually, he may recommend those places even if you have two nights.
With more time, Balestrand can be considered. I think just about everyone agrees it's a more pleasant place to stay than Flam. After all, Flam gets monster cruise ships; it's a workmanlike town in a magnificent setting. But Balestrand is on the north side of the Sognefjord, and the various Nutshell transportation links are on the south side. For folks without cars, I think the only practical way to cross the fjord in the area around Balestrand is on the once-day express boat that links Balestrand to Flam and also serves Bergen. So there's a substantial reduction in efficiency if you don't have a car and opt to stay in Balestrand.
About the only transportation links in the area around Flam running at any frequency at all are the Nutshell components and the bus between Flam and Aurland. Therefore, those with limited time who want to do the scenic legs of the Nutshell route and have no car almost have to stay in Aurland or one of the towns served by the Nutshell transportation; it's very difficult to travel via public transportation to one of the Nutshell transit points from elsewhere. I don't think there's lodging in Myrdal, so it isn't an option. Working from west to east, that leaves:
Voss: Not on a fjord, but has a fair amount of lodging and outdoor activities that might be appealing. Frequent mainline rail service to Bergen.
Gudvangen: On a fjord but I think with limited lodging. You have the Nutshell buses connecting to Voss plus a few others. Seems not to book up as fast as Flam.
Flam: The most convenient place to stay, thus rather expensive for what you get and probably the first to sell out. The youth hostel seems well-run and has a few rooms with private baths.
Aurland: Said to be viable because of the bus service to Flam, which is quite close. I haven't dug into bus schedules or lodging in Aurland myself.