We are trying to decide between 2 apartments. One is on the Arno River (the side with all the site) and the other is near the Duomo. Which do you think is more convenient. the river one is a little nicer
I'd take the place on the river any day (if you don't mind the mosquitoes, which will be in both places anyhow). My cousin has a place on the Ponte Vecchio and in Summer it's so much cooler there. I guess the cooling effect of the water works. Besides an apartment on the Arno is the ultimate location also for the view. I also grew up along the river Arno (although my place was separated from it by the river park in front.
The Duomo area is more convenient in general but can be a little noisy. The Arno is long by Florence and could involve alot of walking depending where you are proposing. If nr Ponte Vecchio bridge either will be fine.
Take the one on the Arno River if it is nicer. The great thing about Florence is, it is a small city and you walk every where. No cabs, just walk. It is a very easy city to get around and you will enjoy waking to everything. It is not like London or Paris or Rome where you need to take public buses or trains, you will enjoy the city, big enough to see lots of things and places to go and museums and churches, but small enough that you walk to places and then rest at a wine bar or cafe for a drink. Have a great time