Trust me people - stay on The Strip.
It's so much easier (and you can get decent prices, esp during the week.) Try Expedia & those type websites. My brother's gotten really good deals through cheaptickets.com (I believe he stayed at Mandalay Bay for $65 per night.)
Off strip is a huge pain - like someone said, your hotel may have a shuttle, but it may only be hourly; it may not run after midnight; you may have to meet the shuttle in a certain place at a specific time to get back. And you CANNOT walk TO the Strip, for the most part - it's surrounded by highways & busy streets with no sidewalks.
It's not like other cities - everything looks really close on the map, but sue to the immense size of these places, it's deceiving. However, you can walk up & down the Strip itself.
Downtown may be the only exception - I believe there's shuttles between downtown and the strip all night. And a cab shouldn't be that bad - $25 maybe? Not sure about the newer area (Rio, Palms, etc.)
Cabs are easy, not terribly pricey. The only drawback is that you can't get them curbside like every other city. It's a traffic law.
You have to go to one of the hotel entrances to get one - not a big deal if the entrance is close to the street (Boardwalk, Circus Circus) but the bigger hotels (Luxor, Caesars) are set WAY back - some actually have people movers to take you from the street into the place, but they'll throw you into the casinos first & sometimes it's damn near impossible to find your way out.
The bus is very easy, very cheap, runs up & down the street all day & night. I wouldn't recommend taking it late at night though.
Scary. The trolleys are good too, but they only make stops at certain hotels & they don't drop you off on the street either - they put you at the hotel's entrance, so you may have to walk 10 or 15 minutes to where you need to go. I think it's $3 per ride no matter how far you're going; I think they have an "all day unlimited pass" too, not sure how much.
Another option is the monorail, which runs behind several of the larger hotels. It only connects certain ones, though - MGM, Paris, Bally's, Caesars, off the top of my head. It's great if you're staying at one of those hotels; but it doesn't run all night AND last time I was there it was shut down for repairs both times we tried to get on.
So it's not 100% reliable. Here's a link:
monorail