The NuVinci system is fantastic in principle and one day all bikes might come with it, but we aren't there yet. As the system stands there are a few matters that might not make it the answer to your prayers of an easier time going up hills:
For hilly terrain you need gears - it goes without saying. The steeper the hills the bigger range of gears - going up you may need a 'granny gear' and going down the hill you need a big gear (unless you don't like speed and coast).
This is the potential problem area with your intended application. The NuVinci hub has a range of 350% - exactly what that relates to depends on your spocket/chainring choice. Meanwhile, with a Rohlhoff or basic derailleur setup you are going to get a range of around 530%. Touring bikes and XC-MTB's usually come with an even greater range, however, do you use the 'granny ring'?
Note that early adopters of the NuVinci hub seem to be primarily in Denmark and the Netherlands, where the terrain is flatter than the North Sea.
There is also the small matter of efficiency. With a derailleur gear setup you can get an amazing 98% efficiency when on the middle ring and middle sprocket, marginally less for other 'sensible' gear combinations, even if you have not 'lubed' in a while. (The problem with studies on this is that they also include 'silly' gear combinations such as small sprocket and small chainring where the hideous chainline makes for an inefficient system, giving a wider efficiency range than is realistic). No hub gear system can improve on derailleur efficiency levels and the NuVinci FAQ side-steps giving any useful figures, preferring to make comparisons with existing hub gear systems, for which 92% is roughly ball-park. Personally I could contend with that on rides through town where gears are for getting up to speed but not for sustained hill climbing where 5% loss would mean 5% slower.
Weight is another area where the derailleur rules supreme. At the moment the NuVinci hub is relatively heavy - I think the latest systems are 1.5Kg heavier than an average derailleur setup. In my opinion weight really does matter on hills in a way that it does not if riding on the flat. I frequently pick up 2 litres of milk at the bottom of the hill where I live and it does make an appreciable, albeit not show-stopping difference to how I attack the hill.
Variable range gears. Personally I have no problem shifting gears on a 9 speed sprocket, thanks to the wonders of 'Hyperglide'. I also find that there are enough of them and I have no need for gears in between the gears that I have. For me an infinite amount of gears sounds good, but in practice I think the 'need' is over-hyped. I don't find myself changing up/down to find myself spinning furiously or plunging away completely out of sensible cadence. However, I can see how the NuVinci would help those that don't change gears that cleanly, i.e. not anticipating the need for the middle ring at the base of a hill.
Maintenance. Not a lot is needed for the NuVinci system because it is a hub gear. If you are running bullet proof tyres you won't even need to get the wheel out for punctures. However, if you did have a problem and needed to take it to the shop then they would be stumped.
To conclude, you will have extra weight, lower efficiency and a reduced range of gears. Despite the benefits of CVT with smoother shifting, reduced maintenance and not having to match your cadence to available gears, you are not going to get round the fundamentals of weight/efficiency/range.
My recommendation is that you try an electric assist bike such as one of the models made by Giant. Although they weigh a lot they are amazingly nimble and you can pedal as much as you want to on one.