Your best option for getting close to giraffe's is the Wanyama Safari, which is open to all guests at the AKL, (book early as it is very limited in group size). When we did it we had giraffe's close enough to touch. You ride in the bed of a truck, which has a high roof and has benches to sit on. We were able to stand as they move very slowly. There was a naturalist driving and one in the back of the truck with us. We were able to get very close to all the animals. They even went out of the way several times to make sure that we able to see baby okapi and waterbuck. The dinner at Jiko was also over the top.
We did both the Sunrise and the Wanyama Safari's on the same trip. Both were good, but we thought the Wanyama experience was a little more personal, (smaller group), we got closer to the animals that they have at the Lodge and enjoyed the experience more.
Now, if it is lions and elephants that you want to see, you can only get that on the Sunrise Safari.