Ok, first piece of advice. Don't stay near the Regency area, come to think of it, I don't think that there are any hotels there. I would look over in the Town Center area, which is not too far from the Regency area and not far from the beach either. THat area is fairly new and I don't get over there very often. Do a google search for The Town Center, Jacksonville, FL. Hopefully this will help you. If this doesn't help do a Google for the Apple store in Jax, or PF Changs. These are both in the town center and you should be able to find hotels. Again, DO NOT go into the Regency area by yourself or with your daughter at night. THis was a good area at one time, but know not so much. You will be fine during the day, but I wouldn't recommend it so much at night.
Also, the Town Center has a lot of great shopping and restaurants. I really haven't been to our beaches in years and years, we usually go south to St Augustine, but I do know that they have done a lot of work at Jax Beaches, so I am sure they are nice.