Been living in Henderson for a few months now.
My outdoor staple rides are ether west on Highway 160 toward Blue Diamond/Red Rock/Mountain Spring or east toward Lake Mead, Hoover Dam//Arizona.
Running has a couple trails out in those areas (Red Rock//Lake Mead), but a couple trails closer to the city's southside: Amargosa Trail (trailhead on Shaded Canyon), Sidewinder in Sloan Canyon. These folks get together to do trail runs frequently (
https://www.facebook.com/.../trailrunning.vegas/).
As for swimming, I use the Henderson Multigenerational Pool out in Green Valley. T/Th AM LCM, otherwise SCY--good weekday hours, weekends are a tad scant for me. Lake Mead for OWS, a couple beaches, but the go-to is Boulder Beach.