Florence running recommendations

I'm not a runner but along the Arno, up to San Miniato, or as far as Fiesole were favorites for a couple of friends who run cross-country.

Not much available in the historical center. Just narrow streets and alleys, with no trees, often filled with millions of tourists worse than Disneyland on a summer weekend.
I can only tell you where I, and all Florentines in general go. You decide based on what will be closer to your location.
On the west side, west of Ponte alla Vittoria, there is the Cascine Park. Probably the most popular spot for runners. Plenty of paths there with no cars, all in the middle of trees.
For the Florentines who, like me, lived East of the city center, there are the parks along the Arno, pretty much starting East of Ponte San Niccolo'. You can run all the way to the Ponte di Varlungo (via Marco Polo) cross the bridge to the south side of the river and come back west to the city center through the Parco dell'Anconella, all along the river. Then at Ponte da Verrazzano I would cross the river back to the northern bank and continue west to the city center. You can also stay on the southern bank all the way to Piazza Ferrucci, then go uphill to the tree lined Viale Michelangelo to Piazzale Michelangelo and continue down to Porta Romana through Viale Galileo. Then from Porta Romana you can come back to the tourist zoo.