Definitely don't go to Vegas. It's so boring there. 
It's one of the cheapest options actualkly 
However people I know have simply stayed a few days then connected to LA or San Francisco.
I'm getting Glasgow to JFK via Amsterdam at a good deal now, for early December. I'll look into that.
I'm going to disagree with Paul and say that Vegas is fun, at least for a few days. I went there for my final spring break in college and had a blast. Just going around and seeing the various theme casino/hotels on the strip is fun, and will take you a couple days at least. I did that largely on foot. There's also a lot of great shows to go see. There's tons to do and see, so you don't even have to gamble, though gambling can be quite fun if you're not stupid about it.
Staying a few days and then taking another flight like those people you know have done might be a good option too.
I'm planning to take a vacation some time in October. My first choice is a cruise, but getting my birth certificates so I can get a passport is taking longer than I would like, so that option might not work. I'm thinking of another Vegas trip as an alternative.
A few tips for gambling and shows if you decide on Vegas:
1. This applies to any place you might go gambling, not just Vegas - set aside how much money you are willing to lose in advance. That's your gambling money, and under no circumstances should you ever withdraw more from your bank account for this purpose. The house always has an edge, so go in thinking that you will lose it. Gambling has a chance to win, but primarily you should have the attitude that you are getting an entertainment value from it. This is THE most important rule. (note - winnings don't necessarily count, you can gamble those back into the casino if you want) For me $700 was enough for three full days.
2. If you hit a decent sized win on a slot machine it's time to cash out and move on. "Decent" in this case means about $100 or so. The machine will likely just take it back if you keep playing.
3. For slots in general, try to find a high-payout machine. The machines today are based on random numbers, and each one is programmed to pay out at a certain frequency. Some pay out higher than others, so if your "luck" on a certain machine sucks try another one. You can Google more information about this - these machines are usually in certain places in the casino, so knowing where to find them helps.
4. In general if you get a nice payout, from slots or otherwise, rather than putting that back into your gambling pool take a bit out and use it for your food expenses.
5. Get a comp card of some kind - groups of casinos use these, especially at slots, so you might get a few freebies when you lose money on gambling with these.
6. For a show, I recommend seeing the Blue Man Group at the Venetian. It's a really fun show.
7. One last thing - if you want to save a bit of money stay in a hotel off the strip. They tend to be a bit cheaper, though many of them are still very nice. I recommend this one for that purpose:
http://www.southpointcasino.com/
