LH738 - There is a promenade between the hotel properties in La Caleta and the beaches (MoritzK's reply about the beaches being public explains why the path is there). The hotel has a key card controlled gate to the path at the back of the resort. There are plenty of people walking and jogging along it, and I would suppose (but didn't try it) that you can go all the way along to the next town - Las Americas - though God alone knows why you might want to.

WaltherVonDerVogelweide - All the rooms have balconies, and all have tables and chairs there.

Incidentally, the map on the hotel's website makes it appear that the hotel is on the wrong side of the motorway TF1. Rest assured it is right on the coast. I mentioned it to the front desk staff, and they said they would pass the message on, but clearly these corrections take time.