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Might I recommend the likes of:
http://www.macdonaldhighlands.com/re...ry/villabella/
Don't worry about security... I can house sit for you while you're away. [img]/images/graemlins/smile.gif[/img]
More seriously, it's hard to know what you want. Safe and very near the strip are mostly mutually exclusive without spending lotsa bucks for a 24x7 guarded highrise condo. Of which there are many sprouting. Plan to start at $400Kish for like 600sqft and go up from there, though not proportional to square footage. You can get 1500sqft condos near the strip for ~$700K, though you can also spend probably $1.5M on 1500sqft, too; all depends whether you want Regency Towers sorta basic condo or Park Place sorta floofy condo.
Going further out, One Las Vegas condos (that's the name of the thing, ONE LV) are going up right now a few miles south on the strip. Except during rush hours, that's about 10 minutes from LVBlvd/Tropicana. And that's about far enough out to begin to think about houses and safe together. For about $400K you can have your basic 2400sqft, 4BR sorta house with a 0.1acre yard. Adjust up and down depending on home size, yard size, spiffiness, neighborhood and age.
Going a bit farther out you'll begin to reach the areas most folks will tell ya are most pleasant...Summerlin, Green Valley, or other parts of Henderson. But Summerlin and the more distant parts of Henderson are probably not within your 15-minute radius even if the lights are good and there's no traffic. As well, folks have previously suggested areas a few miles east of the strip around Boulder Highway as safe and affordable--that's outside my normal travels.
There are also a few spiffy condos sprouting around downtown if you like that sorta urban-renewal thing where they drop a tower full of $700K condos smack in the middle of a fairly blighted area surrounded by crack houses.
All just my uninformed opinions. I'm not a real estate agent, I don't invest in Vegas property, and I don't travel around window-shopping for houses and condos much. I just live here and these are the basic beliefs and biases I've absorbed.
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Great post, I am also looking into LV RE and found this very helpful.