Down in the lobby they have a tv with kid chairs for the kids to relax as well as adult sized chairs in front of a fireplace. It's so relaxing and even though the rooms are nice it beats sitting in the hotel room. They have an arcade there as well. Then they have a fast restuarant by the pool and an area where you can sit outside and I think you can see a slight view of the DCA park from some of the seating area. Storytellers cafe is a character dining restuarant. There is a bar area down just off the lobby area as well as a spa in the Grand Californian. Also there is cool stuff going on at the other hotels too they would just have to look up whats going on or just walk over to the other hotels to find out. Also Downtown Disney would be a good place to go if they find everything at the hotel wasn't enough.
Sadly, the arcade is no more-they moved their work out equipment to that spot. Just to clarify for the OP: Storytellers is a good casual table service restaurant that has a character breakfast buffet. Lunch and dinner are not character meals. Whitewater Snacks is near the pool and DCA entrance--we usually grab breakfast there IF they're open before EMH. Napa Rose is lovely for fine dining, but with a 1yr old? I'd probably pass. Can't use Pinocchio's Workshop for childcare, because they have a minimum age of 5y.
Agree that the fireplace in the lobby is a cozy place to be--even when it's blazing hot outside!!! My kids always make a beeline to the miniature rocking chairs they have set up by the TV, while I'm doing check-in. There's an outdoor fireplace (just on the other side of the wall from the lobby fireplace), though I seem to recall it's a designated smoking area? But, at night, that's where they offered movie night (they set up a screen). We did this a couple of yrs ago, and they had pillows and sleeping bags laid out for the kids. We brought our kids down in their PJ's. Though, looking at the website, it appears they've moved the movie night location to the 5th floor terrace near the lobby. At the end of the day, DH likes to grab a drink from the Hearthstone Lounge and sit & listen to the pianist in the lobby.
The 6th floor balcony that was mentioned previously with the view of WOC (& they pipe the music in for the show)-it's in the DVC wing. The first time I tried to find it, I was unsuccessful. It's a bit of a walk from the lobby.
Oh, and there's the Grand Quest, which is sort of a scavenger hunt.
This page provides more info about some of the activities:
https://disneyland.disney.go.com/hotels/grand-californian-hotel/recreation/