Another fan of Airbnb here, especially for long-term stays. Many of the listings give a discount off the nightly rate for stays longer than 28 days (I *think* it's 28 days, might be 30). You'll see the discounted rates if you search based on your full stay length.
We just booked a stay through Airbnb in Santa Barbara for a month in a nice walkable location. Some locations (SB is one of them) have restrictions on shorter-term rentals in certain zones, so it's good to do a little research when considering popular locations to make sure that you aren't booking something illegal.
Previously we have stayed 1 month in Copenhagen and 1 month in Stockholm using Airbnb, both very positive experiences.
In 2014, we found a great apartment on Airbnb in Barcelona and ended up booking it for 2 months through its proprietary website (they offered a slight discount this way, but it was a bit more risky). Also a great stay, right in the heart of the Barri Gotic.
In 2011 we booked 10 weeks in Paris through an agency called Paris Attitude. It was an amazing location, but they didn't disclose that the place was for sale before we booked so we had to deal with multiple showings while we were there. It was a minor inconvenience, but something we ask about now when we book.
We prefer to stay at places that have multiple reviews. I feel a little more secure knowing that others have stayed at that location before and had a good experience, although if a property is a new listing the owner might be willing to bargain for a longer term stay, as kgtest mentions.
The other thing with Airbnb is just to be aware of the cancellation policy for the rental. Definitely read it through before you click to book, especially if your plans aren't set in stone. Some have a strict cancellation policy where you forfeit the first month's rent if you cancel.
Congrats on your retirement and enjoy your travels!
