Finding an apartment rental?

Do you have a specific city in mind?
Often when you search for stays through Booking.com, you will see the name of the local agency operating the apartment on the listing. In the past, I have then contacted those local companies directly. Just an idea--good luck!

Thanks.
We are very tentatively looking at Valencia--trying to find a good balance between interest, sun/warmth, and places that are new to us. Two years ago we spend a very enjoyable six weeks starting in Malaga, then making a small slow loop via Vejer, Sanlucar de Barrameda, Cordoba, Antequera, and back to Malaga. Thinking that this year we'll try the more south-eastern side.

I am not clear if you are staying in one place for six weeks or moving along, but either way I am jealous, lol.
I think Valencia would make a wonderful city break in winter, but I am not familiar with that region for the exploration part.
To help practice Spanish (and satisfy my need for cheesy tv), I am currently watching a show on Netflix set in Valencia (kind of like ER in Spain) -- it's called Respira. Unfortunately most of it is set inside the hospital, but occasionally you get glimpses of the city or attractions like Albufera Natural Park.
The closest I have been is Cuenca, an hour on the train, lovely gorge-set and artistic town.

We use Airbnb for 2 or 3 week stays. We've used it about a dozen times and never had a problem. BUT- you do need to do your homework. Not just picking only highly rated places but also reading as many of the reviews as I can, because sometimes you can get clues about things even in a 5-star review. Does it have an elevator? Is there street noise? Etc. You'll read 10 glowing reviews and in the 11th one they'll say there's 70 stairs up to the apartment, or it's right above a bar where people hang out in the street at all hours.

I also try to figure out exactly where the apartment is, by looking at the pictures, the ones shot out the window. Then I go on Google Maps and use Street view to find that apartment. I have never failed to find the exact location. Then I find nearby grocery stores.

So, what I am saying is, I think Airbnb is perfectly fine for a 6 week stay but if you are going to make a 6-week commitment, you have to do your homework.

By the way, we are also heading for Valencia next year.

Let me suggest that, when evaluating apartments, you do not discount those in the Quatre Carreres district. Are they quaint with "Spanish charm?" Not at all, but the lodgings there tend to be new and modern, with plenty of amenities, which in our experience is very helpful when staying for several weeks. Plus you are close to both the fabulous Turia Park and the Ciutat de les Arts i les Ciències and Oceanogràfic, two facilities one should allocate plenty of time to IMO. Public transit or shank's mare get you to the old city very quickly, and proximity is also excellent to the Maritime area and the Malvarossa Beach. We found a superb place on AirBnB to stay in the Quatre Carreres for about two weeks last summer. Note: large supermarkets are also available in this district, which is important if you don't plan to eat all meals in restaurants.

Thank you all!
@valadelphia--thank you for the TV suggestion. We're working on our Spanish too, but it's a slow process. A show that combines language learning with scoping out a future travel destination is a great suggestion.
@the other marty--appreciate the google photo suggestion, as well as the grocery store search. One of the advantages of being based somewhere for a bit longer and having a kitchen will be avoiding spending all our time in restaurants. Which is not to say that don't intend to try as much delicious food as possible, but...budget... Also glad to know it's somewhere you're planning to go. As I said in my original post, this is still all rather tentative and unformed right now, but appreciate knowing that Valencia is considered a worthwhile destination.
And @jbhbucks, thank you for the particular neighborhood suggestion. When we were in Vejer two years ago we stayed for a week in a house with a lot of quaint charm, and only 3 fuses. Having the stove and a few lamps on at the same time was fine, but then I tried running the clothes washer. Oops. Modern amenities in a pleasant neighborhood will be helpful for a longer stay!