If you had transportation, I'd recommend the Henderson Competition pool at the Multigenerational center (about 20 mins drive from the strip).
http://cityofhenderson.com/...igenerational-center On the north end of the strip, there is the city of Las Vegas Municipal pool:
http://www.lasvegasnevada.gov/Find/21066.htm There is also the pool at UNLV:
http://www.unlv.edu/srwc A bit pricey for 1-day pass.
Bike rentals ... Pretty much any bike shops.
http://lasvegascyclery.com http://mcghies.com http://www.bikeshop-lv.com (Lots more than these)
FYI you can bike to the multigen and bring your bike into the pool area while you swim.
Finally, you could drive to Boulder Beach and swim in Lake Mead.
Running on the strip ... No great areas other than streets. But, you can get to the track at UNLV (near the Hard Rock).
If you rent a bike ... You'll get some good rides from the shop ... But biking to Hoover Dam and Pat Tillman bridge is a great photo op.
Hope this helps.
John