Forest or Park?
I recommend all of them - they all have loads of scenic places to see. If you want high elevation, the Alta trail, the Twin Lakes trail, the Lakes trail are all excellent. If you want big trees, any of the grove loops have their share of huge trees - or you can backpack out to Redwood Meadow. If you want waterfalls there aren't so many in the park, but Mist Falls and Tokopah falls.
If you want to include trails in Kings Canyon, most of those out of the canyon itself are steep and strenuous. Redwood Mountain grove makes an excellent 10 mile day hike or an easy overnight trip.
Fire bans aren't lifted until enough rainfall to reduce the risk - I doubt that will happen til well into winter.
I'm going up to the Tablelands myself this weekend - I won't be making any fires, it's well above 10,000 feet, and I'll be perfectly fine with that - some of us find the scenery so enrapturing that it's frankly too much nuisance to bother fussing with a fire.