I think the average budget will be 10000yen per person if you enjoy Yakiniku dinner in Ginza. Here are some Yakiniku restaurant for which the budget will be lower as 5000yen per person.
Pyon Pyon Sya http://www.pyonpyonsya.co.jp/
Maruushi Meat https://tabelog.com/tokyo/A1301/A130101/13138388/
I also recommend you to try lunch time, so you can enjoy high-grade Yakiniku restaurant at rather reasonable price.
If you are going to dinner with kids in Ginza, your choices may be limited to chain stores. Pyon Pyon Sha or Gyukaku would be safe choices.