Florence on $85 a Day - Best City View

For the most sweeping views of Florence, take the # 13 bus from the central city area (the tourist area) to Piazzale Michelangelo. 
 This is a well-known viewpoint with lots of kitschy tourist stands and over-priced food and drink, but the view makes up for all of it.

From Piazzale Michelangelo, you can see the Otrarno area where Boboli Gardens and Pitti Palace are located. 

To get back to centro, take the #12 bus. 

Practicalities -
Buy your ticket at any Tabacchi store. After you stamp the ticket in the machine on the first bus, you have 90 minutes more in which to use it again (no need to re-stamp), so you should only need one ticket to go to, and return from, Piazzale Michelangelo.

Tabacchi stores, dotting every street in Italy it seems, are very important spots for tourists.  This is where you buy transit tickets, phone cards, and stamps.