Most of my posts so far have catered to the infamous "Las Vegas virgin" and that's probably as it should be, but, based on my experience, most people who go to Las Vegas once will go back again....and again. It's an addiction.
The Las Vegas Strip is one of the most exciting and energizing places I've ever visited but it can also be exhausting. There's a reason most people only last 2 or 3 days here. It will just wear you out and come close to killing you if you aren't careful. But, if you want to really relax and enjoy your vacation, then maybe you want to get off the Strip a bit. That's usually what I do and I have a great time doing it.
One option is to stay "downtown" and there is quite a bit to do there if you chose to do that. All of the casinos are within easy walking distance of one another and there is usually a party atmosphere. That being said, it is a long ways from anything else you might want to see. Most of the hotels are pretty small and, at best, middle of the road sorts of places to stay. The casinos are small and the crowd is not what you are going to find at the Wynn or the Bellagio. Still, free drinks are easy to come by, the rooms are usually comfortable and you can gamble at lower stakes.
For me, I'd prefer a more full-service hotel somewhere off the Strip. And, when I say off the Strip, I don't mean that you are way off in the middle of nowhere. Now, if you want to be off in the middle of nowhere, there are several hotel/casinos that are great places. Red Rock Station is an awesome place, I absolutely love The "M Resort" and the South Pointe is a great place to stay. Even Sam's Town is very nice and I'd have no problem spending a fair amount of time there. But all of these places are a very long cab ride from the action you expected when you booked your vacation.
For me, I like to stay somewhere close enough to the action that I can easily get there but far enough away that I can spend as much time as I want just relaxing in a comfortable place. My recommendations are to look at hotels near the Strip. I really like the Orleans, the Palms, The Gold Coast, the Rio and Palace Station. Pretty much all of these places can give you a full-service casino/hotel experience but are within easy walking/driving/shuttling distance from the Strip.
There are other decent options you can also choose from. Just make sure that you realize that you won't be in the middle of the action. The Stratosphere and the LVH (old Las Vegas Hilton) are good options as well. Just keep in mind that you can gamble and sleep most anywhere. Only you can decide how important is to you to be on the Strip. But, if you've decided you'd rather not, than most any of these places can be a good (and inexpensive) option.