Welcome to Fort Useless. You're going to be in 441st Transportation Company, 24th Battalion, 7th Sustainment Brigade. 24th was my battalion until our detachment moved to SDDC back in March. You're either going to love it here, or hate it.
You'll hate it if you can't stand NCOs who are nice to Privates. You'll hate it if you like going to the range (you'll go twice per year). You'll hate it if you like to be pushed at PT. You'll hate it if you have to eat at the one DFAC everyone eats at.
You'll love it if you're looking for some chillax time (units are ALWAYS deployed, but usually only a company or two, and when you're not deployed it's pretty laid back). You'll love it if you want to sham. Your family is going to especially love it. You won't hardly find a better family-oriented area. Though it does get a little cold in the winter, this is still the South. Days below 40 are rare in the winters. Days above 60 in the winter are common. Your family will never get bored unless you really truly try to be bored. There's just too much to do. There's the obvious - Virginia Beach and umpteen dozens of other small beaches on the ocean, bay, and rivers. Virginia Beach has stuff to do along the beaches as well - fun houses, mini-amusement parks, water park, very fast go-karts, etc. Your typical seaside attractions. Norfolk has some trendy stuff to do - Nauticus, USS Wisconsin tour, NAS Norfolk and the big ships, Jillian's and the rest of the trendy downtown restaurant/clubs. Williamsburg is going to be closer and it has Busch Gardens (tons of kids rides as well as adult) and Water Country USA, the best water park I've ever been to. It's huge. Free for us, too. So is Busch Gardens. There's also a treasure trove of historical sites and museums all over the place. My family's favorites are Yorktown (also a nice, clean, quiet beach), Williamsburg, Jamestown, Nauticus, Virginia Zoo, Virginia Living Museum, and Langley Air and Space Mseum (IMAX). The whole area is called Hampton Roads and is like one giant city made up up medium size ones separated by rivers and a bay, not unlike NYC. Get used to people calling Norfolk "Nah fick" or "Nor fick". It's their city, they can call it what they like. If for some unearthly reason you happen to do everything there is to do in Hampton Roads, there's always Richmond down the road. The only small problem with Fort Eustis's location is that the city we are part of, Newport News, has the least tourist attractions in the area, but all those areas I mentioned earlier aren't far.
After you've been here for a while you're going to yearn for somewhere a little more hardcore, unless you're looking to relax the remainder of your career. However, I guarantee you'll miss it when you're gone somewhere like Fort Bragg or Benning and can't find anything for your family to do.