I had a nice AirBnB experience near La Rambla that I remember being pretty cheap, but we were just two people - one bed.
With all your miles, you seem like a pretty good travel hacker who probably doesn't need this advice, but Chase Freedom (if you have it) has 5% back on Walgreens this quarter. If you're looking to save money on AirBnB, you can buy amazon gift cards and then buy AirBnB giftcards on Amazon.
Or you can get AirBnB giftcards for ~3% off at Raise.com.
If you can justify spending a bit more on an AirBnB, you can save some by shopping at markets to do some home-cooking some of the days of your stay.
There is tons of nice city walking to be done in Barcelona. I like La Rambla and Plaça de Catalunya. Touristy, but lively and fun. Plenty of interesting architecture and buildings to look at like Casa Milà.