OK...so after that whole "great airfare" question, the next one is always "Where should I stay?" As important as that question seems, it really isn't all that important. Or maybe it is. Because "where" you stay is probably far more important than what hotel you choose. Las Vegas has so many hotel rooms, it is ridiculous. What is even more ridiculous is that a very large percentage of them are filled almost every single day. That being said, you probably aren't going to spend much time hanging around your hotel room. As nice as some of them are, you didn't come to town to watch reruns of Law & Order SVU and order room service.
In my humble opinion, if you are visiting Las Vegas for the first time, you need to stay on the Strip somewhere between the Monte Carlo and the Mirage. That leaves off a lot of really nice hotels, both on and off the Strip but you can always try them out when you return...and you probably will return. Because everything is new to you, you are going to want to try to see as much as humanly possible. And, while I am not a huge fan of hanging out on the Strip, it is arguably the single most amazing man-made spectacle in the free world so, trust me, you will want to be there. And you will want to just walk around and gaze in awe at all the people, the lights and the insanity going on around you. The best way to see as much as possible is to be in the middle of things. Hence, my advice.
The Las Vegas Strip is about a 5 mile stretch of Las Vegas Boulevard, marked on both the north and south limits by a sign in the median, the famous "Welcome to Las Vegas" signs you've all seen a few thousand times. As far as hotels go, it stretches from the Mandalay Bay on the south end all the way north to the Stratosphere. But, if you stay at either one of these fine hotels (and I happen to really like both of them,) you are going to be hoofing it one hell of a long way to see all the sights. That's why I've narrowed down your best choices to places where you will be able to see as much as you can without wearing out your shoes. Which specific hotel will be best for you is only something you'll be able to answer after you've stayed there. But, keep in mind that even the "budget options," the smaller or older Strip hotels are likely to "wow" you. You will almost certainly visit somewhere on your journey and think to yourself that this place is just awesome and that, when you come back, you'll just have to stay there. But if you've never visited, that is part of the fun of it all.
OK...you say, but you still haven't told me where to stay! I want a name. I'm poor...I want a great deal. What can I do? I'm going to have to ask you to have another sip of whatever beverage you are drinking tonight, relax, and just trust me here because I'm going to help you. You're poor...I get it. I'm relatively poor too. But, if you weren't, I'd just tell you to lock up a suite at the Cosmopolitan, Bellagio, Caesars Palace or the Mirage. Your chance of getting a "great deal" is going to be much greater if you visit at a time that fewer people want to be there. Go around Christmas-time or in the scorching heat of July and August. Just be prepared for either some chilly temperatures and some closed-down shows or for the possibility that your shoes might melt....seriously.
First, I have to ask you if you are already a degenerate gambler. You are? That's a good thing...maybe. Most of the major Las Vegas casinos are owned my mega-conglomerates who have dozens of casinos and maybe one in your area. Do you already have a Total Rewards card or an MLife card from your local casino? If you do and if you've gambled even a fair amount of money at that casino, you should be able to get at least a discounted price and maybe even a free room at a Strip casino that falls within my geographic range. You may really be in luck if you have a Total Rewards casino in your area (typically a Harrahs but possibly a Harvey's, Showboat or Caesars) and if you've dropped a few dollars in one of their casinos recently. Total Rewards casinos that might be good choices for you include Harrah's, the Flamingo, Bally's, Planet Hollywood, Paris and (if you are really a high roller,) Caesars. Now, if you are fortunate enough to have an MLife casino near you (not as common,) you will want to investigate the Monte Carlo, Mirage, Aria and the Bellagio. All of these places are pretty centrally-located which is what you want. Not all of them are amazing hotels but, remember, that is not your primary concern.
Even if you aren't a degenerate gambler (yet,) several of these hotels offer reasonably priced rooms (particularly between Sunday and Thursday nights) and are good solid choices. So look at the following places for the best deals: Monte Carlo, Flamingo, Bally's and Harrah's. None of these places are the newest or nicest or trendiest places in town but they are all within walking distance of plenty of places that are. You can also occasionally find a good deal at the Mirage, Paris or Planet Hollywood but you'll pay more staying in a nicer place and I doubt it will be worth it to you. The Bellagio, Caesars Palace and Aria are going to likely cost you more than are going to want to pay, particularly if you are going to be there at least part of the weekend.
So there you go. I narrowed it down to basically 4 hotels you should focus in on as places to stay. I'd really look at the Flamingo. It probably has the best location and it also has history as the first major Strip resort over 60 years ago. It is a Total Rewards casino so you might be able to score a good room rate and it isn't a bad place at all. Oh....and on my first trip to Las Vegas, that's where I stayed.