Sam Roi Yot is lovely, but is not Hua Hin. There is very little aside from the beachfront low end or high cost resorts.
Cicada market is at the end of Hua Hin closer to Khao Takaib than it is to Hua Hin town.
Now to answer OP question, please have a look at Agoda, there are many hotels and service apartments that are at historic low cost now. I have stayed at many of the serviced apartments hotels that surround Market Village. Nothing spectacular, but they are solid 3 stars. I feel that I have received much better value at these places than when I have stayed at Intercontinental and Mariott, which are direct on the beach. The ideal zone if you wish easy access to beach is between Bluport and Market Village. There are some reasonable hotels on the beachside of the main road Petchkasem. The best value is on the other side of the road with the new DUsit mid market facility and others. Also, there are many reasonable Thai restaurants in the area. Beware that traffic can be heavy so you will need to use overwalk at market Village, or Overwalk at Intercontinental/Bluport or the pedestrian crosswalk with lights midway between the two at Bangkok Hospital (People slow, but do not necessarily stop). I mention all this because I do not know if the child has strength to walk the 100-250 meters to the beach. They are all easy walks. I recommend the zone between Bluport to Market Village because of the easy access to services, restaurants, food markets, cinemas etc. Inner part of Hua Hin is dead or dying as the city prepares to redevelop the former entertainment venues, many of which have moved towards the market Village to Bluport area.
Despite all the activity, town goes quiet by 10 pm and outside of the bar district, everyone is alseep by 11 pm.
It's a place I like to recharge my personal battery in. Aside from the poor accessibility to airports and awful train schedule, Hua Hin is the ideal place to stay.