I go every year, it's so much fun. Got married there when I was pretty young and get to use it as an excuse to go back and enjoy it.
Hotels are a really personal preference,I like the Cosmopolitan over the Bellagio, I've stayed there for the last 4 years in a row, off again in a few months. It's bang on central, next door to the Bellagio, has an excellent players club if you want to gamble, has good food options and is the only hotel on the strip that has rooms with balconies which gives a stunning view in the evening, especially if you are overlooking the Bellagio Fountains. For me, the Bellagio is a little stuffy and I don't think the casino is as good. But you might prefer it, so do your research.
You've had good tips already about where to visit. A nice place to clear your head is Red Rock Canyon, it's about a 30 minute drive from the strip, you can hike, see some wildlife, have a picnic, watch people rock climbing. Hoover Dam is interesting.
I get a bit fed up with the Vegas food, so I do love to stop at Wholefoods which is just at the north of the strip beyond Mandalay Bay and just have a normal sandwich/salad. I prefer to eat at some of the more local restaurants off-strip, look on tripadvisor and there are some really good authentic restaurants, Thai, Mexican. Saying that, you can't beat at least one trip to the Cheesecake Factory at Caesars and Earl of Sandwich in the mall by Planet Hollywood is a really good, quick, cheap eat.
For shopping, I like the Fashion Show Mall, it's got all the stores we like. I tend to do a lot of my Christmas shopping there. When are you going? November time has some really good pre-black friday sales. Make sure you have Uber and Lyft on your phone, the cars are everywhere and are much better than taxis.