In reply to SteveoS:
The GR20 huts are cheap to stay at, but you need to book to be sure of a place - there's a web site for this, same one for all of them (we went in late July and some were rammed, some weren't). I thought they were all great, with a convivial atmosphere, although the food is very expensive. They have kitchens though, so you can cook if you want.
There is also camping at most (maybe all??) of the refuges) and quite a few people doing it. They are the only places in the national park where you are allowed to camp. They seem to have tents that you can hire - those pop up ones, but once you have opted for camping, they won't let you use the indoor kitchens.
There are several places where you can get up to the refuges, without doing much if any of the GR20. The scenery is fantastic. I liked Petra Piana, which you can get to from the railway stop Tattone, where there is a camp- site and ace cafe making great smelling stew, via a bergerie that makes superb bread and sausage. Come back the same way or via the refuge Onda, to Vizzavona, a couple of stops further along the railway line. This is the railway that goes from Bastia to Ajaccio, diagonally across the whole island, top right to half way down the left-hand side.
From Corte in the centre you can take a bus (a minibus with trailer, actually) via a scenic route to the Col di Verghio, and from there it is three hours or so to the refuge Ciuttulu di i Mori, where the demeanour of the hosts very closely resembles that of the Corsicans as depicted in Asterix in Corsica,and the coffee is the best of the GR20. From the refuge, scramble up Paglia Orba if you feel like it. I did it before breakfast.
I thought Calvi a bit tacky, but after the the GR20, it was very welcome, and as Sean says, you are close to mountains, and the bastille bit of it was very atmospheric.