There are some water areas just on the other side of the road from Vera Playa that attract waders and stuff. I think they are an area that is scheduled for development, but it appears to be on hold.
Just a couple of miles south, on the northern edge of Garrucha is the mouth of the Rio Antas, where there is a lagoon and reedbeds separated from the sea by a sandbar. Best viewed from the beach (you cant see anything but reeds from anywhere else, so it's best to get there early. I've had night heron and little bittern there as well as other stuff.
Just inland from Garrucha there are various tracks and minor roads that are worth a look. I don't know if the rollers will still be around when you get there, but this is a good area for them, as is the stone bridge over the Rio de Aguas just past Turre (a little further south from Garrucha and inland from Mojacar). I had my first Eagle owl from Garrucha - completely accidental. We were admiring the sunset on the last night of a holiday and one flew by.
Cabo de Gata is definitely worth a look. Black bellied sandgrouse, larks etc on the grassland of Las Almoladeras stretching south from Retamar. I had an apartment overlooking it in the spring and we had sandgrouse within 5 minutes walk and stone curlews calling audible from the house every night. Didn't catch up with Dupont's lark (too windy I think), but there were at least two rufous bushchat territories near the road crossing Rambla Morales.
The lagoon in the Rambla had marbled duck (can be awkward to see, check around the bases of the tamarisks - see the photo below. There are two ducks in it - honest.), white-headed duck, flamingos, terns and gulls, including Audouins and slender-billed. Lesser short-toed and short-toed larks in the scrub south of the lagoon.
Sierra de Cabo de Gata, especially around the lighthouse, drips with black wheatears.
The Salinas de Cabo de Gata are good for flamingos, terns and waders, but distances are large and heat haze is a problem
Inland the ramblas around Tabernas are worth a look if you get time. I don't know what they'll be like in September, but in the spring and summer I've had olivaceous, melodious and orphean warblers in various places, rufous bushchat, roller, rock sparrow and various other odds and sods.
It's not a great area for raptors, but there are the odd short-toed and booted eagles and black kites to be seen - none of them as numerous as in other places in Spain. I've seen Bonelli's eagle there too, but only once.