There are many good hikes on Oahu. A few of the harder hikes may be low traffic, especially if you hike mid week when the locals are all at work. But most hikes will probably not give you the seclusion you are looking for.
Some waterfall hikes:
Maunawili Falls in Kailua
Manoa Falls in Manoa
Judd Trail/Jackass Ginger trail in Nuuanu.
You can swim in pools at any of these hikes, but I don't think you can really swim under any of these falls. Bring bug repellent & expect mud. Do not swim if you have any cuts or wounds, as you risk infection.
Other nice hikes:
Makapuu trail in eastern Honolulu
Diamond Head trail - both of these trails are fairly easy climbs with rewarding views. Bring water & sunsscreen.
Puu Ohia in Makiki - a bit less traveled, small amount of climbing, good views of Nuuanu.
Have a nice vacation & enjoy your hikes.
