I would also book accommodations in the Cinque Terre as soon as possible. It's less a matter of recommendations for favorites at this point but being able to land anything which suits budget and amenities at this late date. There's a post in the Italy forum by a gentleman who is also looking for a room in Sept. and having trouble finding availability.
As far as "the hike", there are many hikes which can be done, but some are longer and more strenuous than others, and you don't want to be on the trails if it rains so have a Plan A and B.
They appear to be overhauling the website for the park, and the English tab throws you into a different site that's not very helpful: hope it's temporary just until they get translations done. Anyway, the page for the trails on park website (Italian only) is here, and those which are close are marked with a red andwhite circle:
http://www.parconazionale5terre.it/sentieri-outdoor.php
The trail route most people do is SVA2 (592-1 to 592-4). This is also called the Sentiero Azzurro (Blue Trail) and runs along the coast for 7 miles or so between Monterosso and Riomaggiore. As you will see on the chart/map, the 2 segments between Corniglia and Manarola, and Manarola to Riomaggiore are closed. A piece of trail from Manarola heading towards Riomaggiore is open but doesn't go all the way through.
You can get segment info and location by clicking on any trail on the list, and then copy/pasting the text into an online translator like bing or google translate. " Itinerario chiuso" with that same red/white circle as on the map means the route is closed.
You can also get trail locations and numbers on the map here:
http://www.parconazionale5terre.it/map.php
Click the box for "itinerari", and then click on the blue icons with white arrows.
You do need to buy a pass to hike the trails, and that info is here:
http://www.parconazionale5terre.it/cinque-terre-card.php
Passes can be purchased for the trails only, or in combo with a train pass.
These are park and train combo tickets:
"Cinque Terre Train MS" one day Adults: Euro 12.00
"Cinque Terre Train MS" 2 days Adults: Euro 23:00
"Cinque Terre Train MS" child 1 day: Euro 7.30
"Cinque Terre Train MS" one day over age 70 (senior): Euro 9.70
"Cinque Terre Train MS" one day family: Euro 31.50
These are park only:
Park pass 1 Day Adults: Euro 7:50
Park pass 2 Days Adults: Euro 14:50
Park pass 1 Day Park child 4.50 Euro
Park pass 2 Days Park child: Euro 7.20
Park pass 1 Day Silver (over 70): Euro 6:00
Park pass 2 Days Silver (over 70): Euro 10.00
Park pass 1 Day Family: Euro 19.60
Park pass 2 Days Family: Euro 31.50