The Orleans, Gold Coast, Sunset Station, Redrock Station, and South Point where be where you want to spend most of your time. Texas Station as well. Since Sunset Lanes became Wildfire Lanes, that place went downhill. It was a really nice 40 lane house that had the most competitive league in the city, in terms of regular league and sports/tough shot league. Now it is down to 20 lanes, a pool and dart board hall, and casino.
You'll find a lot of tournaments down there. The True Amateur Challenge tournaments are always a blast. You'll find PBAX leagues and sport condition leagues all over as well.
Get a feel for all of the alleys there: Those mentioned above, plus Suncoast, Sam's Town, and if you're up for the drive, Riverside in Laughlin and Virgin River in Mesquite. They are all in the SNBA, so any travel leagues will also make it out to there.
Pro shops. David Haynes runs one, and K&K is huge there (They have at least 4). So if you want to know where the competitive leagues are, hit one of their pro shops, and they won't steer you wrong.
Also, if you hang out down by Sunset Station, you may run into Wendy McPherson, and she will never steer you in the wrong direction.
BL.