I am planning to go to Hua Hin next month with my family, is there any tourist attraction places that close down due to the mourning period?

As long as you are here after November 13th, most places should be open and many places that have toned down the music or lights. I am planning on being in Hua Hin myself later in November and plan on wearing more somber colors, not wear shorts as much. As I will be traveling with some Thai friends. Pay your respects to the King by letting any Thai you talk to that you are sorry about his death. This is a very hard period of time for many Thai, my Thai girlfriend is reacting a lot more to the King's death than to her own father's death 3 months ago. If that tells you anything. I expect most if not everything to be open but, you never know how people are reacting to the death of the King and rightfully so. King Bhomibol has been on the throne all of most of the Thai people's life and he is revered unlike anyone I ever remembered except maybe John F. Kennedy in the US. Be happy and not loud, enjoy Thailand.

Although the official mourning period is one year, it's only for 30 days after the death that this will affect anything in practice, so if you're going after that (ie. around Nov 11th onwards) then you shouldn't find anything closed down. In any case, the tourist destinations are likely to be operating more or less as normal even during the 30-day-period.

By that date, it is unlikely any tourist attractions will be closed. A few of all kinds of businesses may have limited hours, muted colors, and no booze, but Thai must survive by working, so open mostly.