We live in Orlando so we don't stay on or off property, but we have passes so we are usually in Disney about once a week.
The Wilderness Lodge is really nice. They have a great resturant in the main building! They also do campfires and movies most nights for the kids.
Kidani Village is awesome! There are tons and tons of animals living on the property so there is always something to see/do at the hotel. There are even packages avaliable where you can rent night vision goggles and go out and see the animals playing at night. Soo cool!!
Boardwalk is sooo close to HS. There are also tons of resturants and game places on the boardwalk so there is also a lot to do around there. You can walk to HS or take the boat and it is really quick. It is also a very short walk to Epcot from the boardwalk.
Sorry I didn't really help they are all awesome. My husbands favorite has always been the Beach Club. They used to stay there every Christmas when he was a kid.
With the ages of your kids I would probably reccomend doing Animal Kingdom instead of Hollywood Studios though. I'm assuming you have been there before, because you said it was your kids first time. But HS doesn't have that much for young children (so much fun for older kids and adults!) For the younger two they have Playhouse Disney (a show), Little Mermaid (a show), a Toy Story ride (but you have to get fast passes first thing in the morning as soon as you get there run to it, I haven't seen the line less than 2 hours long in the past two months and that's when the park isn't even crowded!), and a Honey I Shrunk the Kids Playground. There are tons of other things, but some can be a little scary. My almost 2 year old LOVES the Lights, Motors, Action Car show but it does have explosions and lots of special effects so not all kids would like it. She saw the Fantasmic show on Sunday and was a little frightened by it (it is about all the villians getting into Mickeys imagination and making him have nightmares). She was okay on the Great Movie Ride but didn't like the Alien that comes down from the ceiling. We haven't done American Idol or Sounds Dangerous with her. SD is completely in pitch black dark and you have to wear headphones, so I know she wouldn't like it. She hasn't seen Indiana Jones but your 6 and 4 year old would probably really like it, if they are okay with fight scenes and explosions. She did like the backlot tour, but I was suprised again because of explosions. Obviously our two year old hasn't been on Tower of Terror or the Rockin' Rollercoaster ;) but fun for the grownups. They also have a Beauty and the Beast show that she would love, but I have yet to convince my husband to sit through. :) I think I've basically covered everything in the park, but if you want more details PM me. :) I <3 Disney.
My daughters favorite place (other than magic kingdom) is Animal Kingdom she asks almost daily to go see "mickeys animals" it is adorable! There are tons of shows and rides and things to see and do there. It does close early, especially in the winter/spring when it gets dark early so we usually do AK and then go to HS to do the quick things she likes there before heading home. Also if you decide to go to AK make sure you look up what time attractions close so that you can kind of plan your day around what is open longer. Some things close hours before the park closes so that the animals can get fed or whatever they need to do. Also the Bugs Life show is scary. :)
If you can afford it I would do all 4 parks, they are all pretty amazing in their own way. Epcot has a lot more for kids than it used to!!