We go quite often when we find good air faire.
#1 suggestion is to get a rental car and just valet park anywhere you want to go. If you don't want to drive down the main strip (do it once though at least), go a block over and take Paradise, it parrallels the strip. You can get basic maps from any hotel lobby. The buses suck and taxi's are expensive and you will get tired of walking. Car rentals are cheap in Vegas (one year I paid $9 a day).
#2 Get and use a player's card for whatever hotel/casino you like and think you'd enjoy staying some day. They WILL send you special offers since you'll be on the mailing list now. Depending how much you gamble with it they could even send you free room offers and what not.
#3 Go to downtown Fremont street for a bit less busy and older style vegas. We find it very relaxing down there, especially in the mornings. Eat at the Bay City Diner in the Golden Gate for breakfast/late night/dinner/whatever. Don't wait in line, just walk up and sit at the counter. There's a cool light/sound show above the entire street through the evenings. Valet park at the Golden Nugget. Cheap and good blackjack tables can be had at Binions and the Goldgen Gate, and various other ones. Slot machines also tend to be a little more loose.
#4 Bring a specific amount of money for gambling (seperate from your food/accomidations money), that you are comfortable losing. You probably won't, but that way you can relax and have fun with it. If you run out then oh well, if not then yaaay. Please don't hit up the ATM for gambling money.
As for where to stay, unless you are staying at one of the top hotels or upgrading room, I wouldn't pay over $100 a night for a hotel room. Especially right now, they should have deals all over the place. Here's the hotels we like:
Main Strip:
Wynn - Will be expensive, but an incredible hotel with amazing rooms. This is one of those places you'd think of splurging for. The Buffet here is amazing, it's expensive but worth it.
Venetian - Similar to Wynn in luxury and quality of the rooms, about the same price depending on deals at the time. Worth it to walk through the shopping area even if you don't stay here.
MGM Grand - Nice hotel, but retarded huge and too far at the end of the strip. If you rent a car it's not bad but if not I'd stay away. Can be expensive. Really nice though.
Harrah's - Nothing fancy, but reasonable room rates and great staff. Clean and perfectly located in the center of the strip.
Treasure Island - Nice hotel but seems more of a conference/business type of hotel. Good location though. Usually expensive unless they send you a special offer.
Las Vegas Hilton - This is a personal favorite of the wife and I's mostly because it's actually a little bit off the strip. It's on Paradise near the end of the strip that the Rio is on. It's nice and quiet with clean rooms, good staff, and a good Casino for late night relaxed gambling. Part of the Casino is SciFi themed, it used to be where the Star Trek stuff was. (hey, we're dorks what do you want). It's also CHEAP. We usually stay here for ~$30-$50 a night. It's also in the perfect location to hop back and forth from downtown Fremont and the main Strip. (to get to Fremont fast, go stright up Paradise and run into Las Vegas Blvd...keep going on LVB until you hit Carson and go left. Keep going on Carons till it ends at the Golden Nugget valet area, leave car there. 5min drive tops).
Stratosphere - We thought this was a dirty shithole...seemed like the kind of place the freshman college kids thought was awesome...ie shitty.
Circus Circus - Stay away, very very far away.
You really can't go wrong with any of the shows, even the cheap shitty ones are good for a laugh.
If you get a car, take a trip out to the Red Rock Canyon park. There is a nice nature drive through there with many pull offs for short hikes (and some long ones).
Hoover Dam is worth seeing at least once.
We love Vegas and can't wait to go again. Havn't had a chance to the past year.
Have fun!