There are basically 5 hotels in Asbury Park proper.

The Empress Hotel and Asbury Ocean club are practically next to the Stone Pony so they are probably not a good bet for you, on top of the Ocean Club being very pricey.

For reference, I can sometimes faintly hear the Stone Pony Summer Stage from my home 12 blocks away.

All of the hotels are closer than that, but you'll probably be better off at the Berkeley or The Asbury Hotel, or even the St. Laurent (a smaller boutique hotel). If you're staying at the Asbury or the Berkeley, you might be able to request a room that faces North which would also help a lot.

Edited to add: There are several small hotels or Bed and Breakfasts in Ocean Grove which would still be walkable to pretty much any destination in Asbury Park, but I'm not sure how they are with kids.