I never use valet because I have expensive stuff inside the car.
When renting in Vegas, I use Thrifty & my rate is ~$13/day (~$20/day ai) - free day after 8-16 days. I book way in advance, and refare when the rates drop. The Thrifty forum has some of the latest codes. Gas in Las Vegas is cheaper than in California. Arco on Flamingo (just behind Bally's) is not bad, but the Arco on Las Vegas Blvd north of the Stratosphere is cheaper (if you're visiting downtown).

All of these spots (except Caesar's) have very little walking to the entrance.
Bellagio & Caesar's do not have convenient entrances from side streets. The entrances from Las Vegas Blvd are the best that You'll get. Palazzo and Paris are convenient from side streets.

I usually park in one place for the north/center strip and walk 5-15 miles/day, but I often drive to Mandalay Bay if doing the south strip.

--- North Strip ---
Palazzo - the floor counters don't work. Park on level 1 as you turn right from the entrance (from Sands). Area 1a is just around the corner from the escalator. Wynn parking is very good, but I always use Palazzo these days.

--- Center Strip ---
Bellagio - park on the third level (just below the roof). Almost always parking there close to the entrance.

Caesar's Palace - third floor parking almost always has space. However, often you'll have to park 100-300 ft away from the entrance. Longer walk than Bellagio or Paris. When I'm doing Pure in the evenings though, I like to have the car at Caesar's.

Paris - third floor usually has spots pretty close to the entrance. Easiest to drive into Parking from the side street east of the Strip. Planet Hollywood parking is soooo far away (10 min walk through the entire mall) - it's easier to park at Paris & walk to PH. Avoid Flamingo parking - it's a mess.

--- South Strip ---
Mandalay Bay - unless there's a major concert, park on the 2nd floor close to theHotel entrance. Usually a spot just 20-50 ft away from entrance. Excalibur and Luxor parking spots are muuuuch farther away from the entrances. New York New York's convenient, but I've only parked there a few times.

--- Downtown ---
El Cortez parking removed the validation requirement ~2 years ago. Super-convenient for the East side of the Fremont area. I only park on the west or center downtown if I have a room at Golden Gate or Binions & can use their lots for free.