I've been in Vegas in January for a few days (also stayed on Stratosphere). Make sure to visit Bellagio, Caesar's Palace and The Venetian, I liked those the most. I'm not very sure about eating places because during the day we usually went somewhere else like Hoover Dam and other nearby places.
Oh, not sure if you'd like it, but we went to a nice Gun Store where you know, you can pick your weapon and fire at targets (they have a nice variety of guns. including WW II etc). I'm from Brazil too and I have to say it's pretty hard to find a nice one here!
When you get there just make sure to get one of those little ad books, you can get tons of discounts and ideas for nice things to do in those coupons.