david,
To begin with, I'm not sure you'll be able to take a Bus to an Agriturismo unless it's relatively close to a town that has a Bus stop. The proprietor may be willing to pick you up there, but if not you may have to rent a car. I'm not too familiar with Agriturismo's as I usually travel solo so have never stayed at one.
For a regular hotel in Florence, I'd suggest checking the Guidebook listings or Trip Advisor. One night is not really enough for a place like Florence (IMO) as there's so much to see. You may only arrive there in mid-afternoon, which means that you'd only have one evening to see the city.
Finally, with hotels in the Cinque Terre you'll first have to decide which of the five towns you want to stay in. My favourite is Monterosso, which is the largest of the five towns and therefore has the greatest number of hotels and other amenities (and also the best beach). Monterosso tends to have more "conventional" hotels (many serve breakfast) while the other towns tend to have more informal lodgings such as small B&B's and rooms (some of which don't serve breakfast). You can also check the Guidebook listings for places in the Cinque Terre or try to find something from THIS List. There's a similar list for Vernazza. I'd recommend getting something booked in the Cinque Terre ASAP!!! For travel in June, you may have some trouble finding a vacancy.
Good Luck!