With a car, you can easily get from Bergen to Balestrand to Geiranger. We did it by driving on several of the National Tourist Routes including Hardanger and so took in even more great scenery before we got to Geiranger. Anita is certainly correct that it is faster getting to Geiranger from Alesund, but you do miss a lot of good scenery in between. And Anita is correct about the "drop cost" of rentals, so you need to work that out.
IMO seeing the Geiranger fjord from the water, not just the roads into town, is a must. I generally don't mind cruise ships, but Geiranger is so tiny that I'd personally not want to spend much time there with several hundreds (or thousands) of my closest friends. For the low cost option, I'd take the Geiranger-Hellesylt ferry (on foot). Once you get that inexpensive, but splendid mini-cruise done, there's very little of interest in Geiranger. I agree with Anita that Trollstigen (north of Geiranger on Route 63) is good. However, if you can go south of Geiranger on Route 63, you can take the side road up to Mt. Dalsnibba (for a few extra NOK) for an amazing view that is even more stunning than Trollstigen. On a clear day on top of Dalsnibba at 4800 feet you are up with all the tall snowy peaks around the Fjord, and you can see all the way down to the town at sea level. The Trollstigen summit is around 1400 feet lower and I don't believe the view is all the way down to sea level. There are tour buses from Geiranger up to Dalsnibba for the tour ship crowds. It must be an amazing drive up to the peak in a bus, the hairpin turns are incredibly tight. But dozens of buses do it every day in the summer.
Whatever you choose to do will certainly be wonderful. It's hard to go wrong in that part of Norway. Enjoy.