Totally worth it to go to the Woodland Zoo. It's much superior than the GVZoo but smaller. You can take a lotta good photo shots there as some of the exhibits do not have fences so unlike the GVZoo, you can see the animals up close and personal. The only thing I didn't like is the crowds. I would recommend that you go during the off season days when it isn't so hot and crowded.
The highlight was the giraffe feeding. The kids got to feed the giraffes though we had to pay $5 each. Under 2 years old is free. Bloody rip-off but if you've never fed a giraffe before, it's worth it.
Woodland Zoo costs us about $15.00/person plus $4.50 for parking. Food-wise, you should pack up your own lunch but you can defnitely get burgers (mediocre), turkey hot dogs, pizza whatever there. EDIT: Forgot to add, if you get their pamphlet at the hotel, they'll give you $1.00 off per person.
Qui, very far from the Space Needle. You would need to take a car or public transport there. Getting there isn't so bad but it's quite a drive from downtown Seattle.