So, here's the official report on water sources for the North Rim:
https://www.nps.gov/yose/planyourvisit/wildcond.htmIt's usually pretty accurate for this time of year.
I'm not quite sure how you mean "east or west" from North Dome (you mean like east towards Olmstead/Watkins or west towards Yosemite Creek?), but off Porcupine Creek, unless you want to drop way down to Lehamite Creek and then climb back up to ND, just go center left on the easy trail from the big junction about a mile and a half in. Past that point, and before the junction to Indian Rock, is Royal Arch Creek. You might find some water up higher, on the trail about 1/2 mile in, maybe not, according to the report. If you have water, you can go out to Indian Rock for camping or down into the saddle out to North Dome. Porcupine Creek itself might have some flow. Otherwise, you can go down to Snow Creek for water, or if you want to camp in the area, go over the bridge and then uptrail for sites outside the restricted area. Always though, that whole ND loop will have several decent sites down at the lower junction at Lehamite Creek, you just have to keep an eye out for widowmaker snags when you set up your tent. There are also a few sites tucked in along Royal Arch on the lower trail segment between Lehamite and ND. Keep in mind that that loop is also basically a day hike, so if where you want to camp isn't close to water, it's easy enough to just hoof it either down to Lehamite or Snow Creek and load up. Just start the hike with a couple liters apiece and see what comes your way, knowing that there's at least a couple guaranteed sources not too far off from wherever you end up.
Overall, for a couple nights out, heading west, I would do the North Dome area and then head up Yosemite Creek a little ways, then backtrack out to your trailhead entry. Or going east, down to Snow Creek, camp above the restricted area, back in the trees trail-right, or up to Mt Watkins if you don't mind a bit of a climb and hauling in some water.