If you want to check out the strip, you could stay on The Strip. There's a site called cheapovegas that................well, you can guess.
But since you're going in April, you're giving yourself plenty of time, congrats on being smart enough to do that!

I would check out the Westgate (formerly LVH, formerly Las Vegas Hilton), just to see The SuperBook. Go to the top of the page, and click on Sportsbooks. It's ranked #1 for a reason. You could take the Monorail from the MGM (or other places), and get dropped off right there. Conversely, you could stay at the Westgate and get dropped off at the MGM, and then hoof it back. It's only 3 miles, but you'll be making plenty of "stops", if you know what I mean.
Tourist things to do? Bellagio fountains are a classic (there's a reason it was in Ocean's 11), and you can get a great view from the 1/2-sized Eiffel Tower across the street at Paris. They even put some camera sized viewing holes for taking pictures.
Make sure you get downtown to Fremont Street, and check out old-time Vegas. If you like standing in line, try the ZipLine.
While downtown, check out the Mob Museum. It's a 3-story building that you could spend 1/2 a day there if you looked at EVERYTHING. But, you can get out in 2-3 hours no problem.
Penn&Teller at the Rio are funnier than Hell!
Check out the Vegas Forum. Scroll through it. There are some locals that impart much wisdom/anecdotes.

Couple of tips: You can walk around with a drink in your hand, but the phrase is WALK, not stagger.
Do NOT jaywalk in Vegas. I saw the cops hand out 7 tickets inside of 30 minutes on East Flamingo Rd near Morton's Steakhouse!
Do not gamble drunk. Gamble during the day, imbibe after dinner.
Enjoy. And then report back.