You want a pullout couch because...? Are you 3-4 adults or 2 adults with kids?
I just did a quick little search on Booking.com for your dates and there are lots of places for a group of 4 adults. You can use the "Guests" box to specify the number of adults and kids.
When you get your basic results, you can filter them using the list of categories down the left side of the screen in a number of ways. When you click on the category, you can see all the options with how many lodgings are listed under them. I think you will be surprised at the number of listings well within your price range. Many are apartments, our favorite choice for 5 or more nights. More room and more flexibility.
I always ignore the stars and go for the 8+ under Review score. Then I sort them by review score although there are many other ways to do it.
I have never made reservations through Booking.com. I have only used it to identify places to stay and then contacted the place directly. I have lost faith in Trip Advisor reviews, but they do often have links to the lodging which Booking.com does not. If TA doesn't have one, I just Google it. Most places will come up in English (they know where you are), but if they don't, there will usually be a little EN or English or British or US or combo flag to click on for English.