I went to Aguilas to watch the carnival in February and March of this year (2014) and was impressed by the Pension Rodriguez. Although it is quite near to the centre it is in a quiet area , only 200mtrs from a lovely long sandy beach with cafes and ice cream parlours.
The room was spotlessly clean and the owner was more than helpful. The rates are very reasonable too.
There are bars , cafes , shops , museums etc (not forgetting the Castle) all within walking distance and Aguilas itself is still very Spanish - NOT over-commercialised - definitely a place for a relaxing holiday.
I would certainly recommend the Pension Rodriguez . More