I don’t have a lot more to contribute to the already helpful info you got above, but had a few comments.
I went to Fook Lam Moon (dinner) on my last trip to HK, and Lei Garden (dim sum) on a previous trip, and neither were that memorable to me. Fook Lam Moon is supposed to be where the tycoons (e.g., Li Ka Shing) hang out, so I met up with a friend there just to check it out But if you were willing to go to places like that, I don’t see why you wouldn’t be able to go to a 2 star - as @moonboy403 mentioned, they’re all pretty casual. My personal rec is Sun Tung Lok - I went to the one in TST twice (dinner and dim sum), and it was tied with Lung King Heen for the best dim sum I’ve ever had (and the two were miles above anything else I’ve had).
Btw, just out of curiousity, I googled LKH’s dress code, and it’s below:
"Lung King Heen is delighted to welcome families with children aged three and above.
Dress code is smart casual for male guests aged 6 or above. Covered shoes, long pants and sleeved shirts are required for gentlemen."
Also a fan of Mui Kee for the congee - the place is quite a hoot! There are old schoolers eating there with their pet birds (carrying the cages in toe!).
I also liked going to Lan Fong Yuen in Lan Kwai Fong for their milk tea (and their toast) but given that the others didn’t suggest it above, I’m assuming it’s because they thought it was too touristy and not worth the hassle.
Lastly (DISCLAIMER - one of the owners is a friend of mine from our NYC days, so take the following suggestion with 50 grains of salt) - if you’re in the Mong Kok / TST area, I would suggest TAP Ale room. They serve casual western food (so should be palatable to the young ones) but they also have a bunch of microbrews, including Young Master Ales, which is my friend’s brewery, but I also understand he’s gotten lots of third party praise! Only suggesting this because you seem to have an interest in craft beers based on your other posts, and Young Master Ales has some interesting (Asian) flavor combinations in addition to the usual ones.
Some encouragement to go to Sun Tung Lok
The toast at Lan Fong Yuen
Mui Kee (the congee looks like congee