Great location
Buses: buy a travel card at the tobacconist less than 50 metres from the apartment and use one of the very many buses into centro which takes 10 minutes. The card covers 10 journeys and cost about 10 euros. It's based on journeys not people - so one card between you is fine.
Taxis: Also cheap - taxi rank less than 50 metres away costs about 5 euros into the centro. Taxi from the airport was 14 euros but on departure we used the train which was 1.80 Euros.
Train: Main station (Maria Zambrano) 15 minutes walk or one of many buses is the high speed line to anywhere.
Walking: just a few hundred metres to the beach or 30 minutes from city centre.
Restaurants & Bars: Plenty - we went to Rocamar on the beach - good fish.
Shopping: Supermarket opposite the apartment or Lidl just one block away

The apartment was clean, comfortable and well furnished - everything we wanted! Couldn't fault anything and would recommend staying here. Probably too far to walk into the city centre every day but easy access by bus. Great promenade to walk down in the evening with lots of bars/restaurants.