Food: Like Silenus said, you can’t go wrong with “anywhere”. Ellis Island has a $7 steak. It’s mediocre steak but it’s dirt cheap and it’s big.
Gambling: I’m not much of a gambler but I love love love craps. BJ is too serious. People get pissed if you don’t play perfectly. People get pissed if you “take their card”. You have to pay attention if you want to play perfect BJ. It’s just not fun. Craps though. It’s almost better if you don’t know how to play. Just walk up and say to the dealer you don’t know how to play. They’ll be happy to teach you, but flip them a couple of chips after your first, second, and third big win. I know at $5 a bet (or higher) it sounds like you’ll bleed chips pretty fast but I’ve always found the money bleed pace to be pretty tolerable. Roulette is social but it’s a little too fast paced and there are a bunch of betting rules that aren’t as forgiving as a rowdy craps table.
Partying: Chip in the couple hundred for a table at a club or don’t go clubbing. You’re either going to end up paying $150-200 for a decent club experience or pay $60+ (cover + drinks) for a guaranteed terrible experience. There are plenty of non-club nightlife to enjoy. Bars, namely. You’ll probably end up spending just as much at a bar as you would at a club (no table) on drinks but you’ll have an infinitely better time.
Sportsbooks. I’ve never had a problem sitting at sportsbooks, or even drinking at sportsbooks but I do see some people hassled. I’ve sat down at MGM, Bellagio, and Mandalay Bay - no questions asked. Sometimes even with a yard drink. I think if you’re dressed nicely (collar on your shirt, no cargo pockets, and no wraparound shades) and you’re not noticeably drunk, they leave you alone.
Cocktail service without the gambling chip bleed: My friend’s tip that I’ve come to love. Cocktail waitresses don’t serve you unless you’re sitting at a table, chips in hand. However, if you go to a bar where there’s a game machine and make it look like you’re plunking down a lot of cash for video poker, the bartenders serve you gratis the same as cocktail waitresses. You’ve got to put in something like $100 into the machine so that the guy can justify serving you free (good stuff too). So stuff in a benji, play a minimum hand, then drink as much as you wan. Cash out. You’re down like $5 from the poker and whatever you feel like tipping after downing tens of dollars worth of free drinks. Hell, if you’re lucky, you’ll come out on top.