See all the free shows, such as the Bellagio Fountains. (Make sure that you get there early, or you may not get the view you want.) If the wind gets too strong or if it starts to rain, the show will not run.
Also, eat at the buffets. Even though it may sound cheap, hotels like the Bellagio have made it into a four-star experience.
I stayed on the Strip at the Luxor for half the time and at the Courtyard Marriott for the other half.
When it comes to shows, do not be afraid to enjoy the expensive ones (if you can afford it). I saw "O" by Cirque du Soleil, but if this does not appeal to you, try Ka or Mystere, both by Cirque du Soleil, and Mamma Mia, a musical that uses the songs of the hit singing group ABBA as its base.
Quick Tips:
When eating, get a big lunch and a small dinner. The lunches may be less romantic, but it will save you a bundle.
Best Way To Get Around:
A taxi might cost you a bit, but it is worth it. The drivers know the town like the back of their hand. They give you expert insight into all the hotels and even a little bit of history of Las Vegas.
If you think you are going to leave the Strip to see the Grand Canyon or Hover Dam and are thinking of renting a car, do not get a convertible in the summer, as it gets too hot to drive with the top down, so you end up wasting your money on a convertible when you could have easily got a spacious minivan or SUV for the same price.