Cinque Terre in Italy

arnegund, where to stay and what to do depends greatly on multiple factors:

What time of year?
For how many days?
What are your interests?
Who is traveling (How many? Ages/abilities)?
What is your per-night budget?

Also, a good guidebook is going to be a great help for the CT and the rest of your Italy trip as well. Look at Rick's Italy book for starters.

Additionally, these resources are good places to start:
https://cinqueterreinsider.com
https://www.apathtolunch.com

I will caution that if your trip is going to be this spring or summer, you're going to want to make reservations as soon as possible as accommodations book up quickly and far in advance.

September, probably 5 days, like to hike, bike, swim, boating, maybe even kayaking.

And it is my wife and I...., no budget set yet. usually moderately frugal.

arne,

As Kathy mentioned, a good guidebook is the best place to start and the RS Italy guidebook would be an excellent choice. I don't know if all the activities you mentioned are available in the Cinque Terre (biking?), but the best choice of the five towns would probably be Monterosso. It's the largest of the five and has the best beaches, so swimming would certainly be possible. Some parts of the beach are free access, and some are pay-per-use, with beach umbrellas and lounge chairs.

Places to stay will depend on which town you choose. Monterosso has the largest number of lodgings, and many provide breakfast so they're essentially a "B&B". The guidebook has listings for accommodations in all of the five towns. Whichever place you choose, booking soon would be highly advisable.

Specifically for the trails, here's the park's website:

http://www.parconazionale5terre.it/Eindex.php

Trail map and current conditions; click on any segment on the map to pull up a description of that particular trail:
http://www.parconazionale5terre.it/Esentieri-outdoor.php

Cinque Terre Cards:
http://www.parconazionale5terre.it/Ecinque-terre-card.php
You will need at least a Trekking Card this to hike any open segment of the Sentiero Azzurro (Blue Path). Two of the four segments have been closed for quite some time and are said to be unlikely to open this season although there's a possibility for the Corniglia>Manarola leg. Still, there are many other trails which can be explored!

The Treno MS card (covers trail use + 2nd-class trains and park buses) can be useful if using the trains even a moderate amount. Trips between villages run about 4 euro a pop during high/shoulder seasons so can add up quickly. If you buy this card, be SURE to validate it before boarding your first train. You don't have to purchase it in advance: can do that at the train stations/TI centers.

I'll second Ken's vote for Monterosso for the same reasons he listed.

We stayed in Monterosso al Mare last year at Il Giardino Incantato, a charming B&B run by Fausto and Mariapia who should give lessons to anyone considering opening a B&B. They were gracious hosts, serving home made Limoncello upon arrival and an incredible breakfast in the most beautiful garden lush with lemon trees and flowers. We are going back to Italy but, unfortunately, they were booked for the dates we needed.

I can also recommend a wonderful restaurant, Ciak in Old Town.

You will love Cinque Terre!

Five nights is long for the Cinque Terre. We enjoyed our three nights which gave us two days to hike.

5 nights might be too much for some but if a visitor wants to take advantage of all sorts of outdoor activities in the region, then it may not be too much. Just be sure that you're not shorting some other parts of your Italian trip to give this one that much time?

My favorite towns in Cinque Terre are Manarola and Vernazza. I love the deep blue water off the rocks in Manarola, and if you are a good swimmer who does not need to be able to touch the bottom of the sea floor, it would be a great spot for swimming. Once I met a woman who was swimming from village to village along the coast.
Manarola and Vernazza are for me more beautiful than Monterosso. What ever logging you decide, I would caution you against getting a place in La Spezia and commuting (with the rest of the day trippers and cruisers).
For hiking there is of course the more famous Monterosso to Vernazza trail (and sometimes it is open beyond). The higher trail Manarola-Volastra-Corniglia is also pretty spectacular and empty of tourists.