The St George Inn is kid friendly. The owner is very nice as well. It is right at the entrance to the city gates in fact. I dont like that its near the tavern but aside from that nice rooms for decent prices last I checked ( which was a couple years back ).Some rooms have a view of the fort ( right across the street) .
There is also always the beachside. There is a Comfort Inn that was always decent and I dont like Comfort Inns at all.
Dont forget to do the Ghost walking tours if you can. Some of them are not to scary and a few go during the daylight. Its a great history lesson and they dont try to scare you at all. One thing cool we saw was the building where the nautical shop is now on St George Street was once a opera house that John Wilkes Booth visited before the assasination. He even carved his initals into the glass window there upstairs in the dressing room. They cover a lot of cool history.
Sorry to go offtopic I LOVE St Augustine!!! If I can help with any info please let me know. I used to live in the town over from there.
Oh Stay away from the Scottish Inn! Its YUCK! I hope they tore that place down.