Acclimating my daughter in Murcia

Cartagena is a lovely small city with a Roman amphitheatre overlooking the sea. About 30 miles from Murcia city.
Also Spanish navy submarine base!

It has been at least five years since I've been there, but we did once live for a couple of years in Murcia (the region - specifically Cartagena). I think it is a wonderful region. And the cuisine is, arguably, the best in Iberia.

For Murcia (city), there are no "wow" sights (in the sense of the Alhambra or Mezquita) but it is delightful to wander for a day or two and there are plenty of interesting places to visit (e.g. the catedral and the casino). All the places and squares you'll want to see are in a compact area.

I've no specific hotel advice. But, staying anywhere in 5-10 minutes walk of the cathedral will put you in an easy walk of all the other main sights. Just an exception is if you arrive by rail or coach - the stations are both about 20 minutes walk from the centre.

The cathedral surrounds and streets nearby are great for food. Outdoors, Plaza de las Flores is beautiful.

As for an alternative coastal place - Cartagena seems the obvious place. There are good sights (certainly a couple of day's worth) and a nice ambience. I'll just mention the Civil War museum which is in the air raid shelter built inside the central hill. Well-worth visiting.

Elche would be another idea.

We stayed not far away for a week. Elche with its palm groves is nice, as well as Cartagena as mentioned above. We liked the Calblanque nature reserve by the sea too. This was our week in the area:
https://slowtravelitalyspain.blogspot.com/2025/04/torrevieja-in-february-trip-report.html