I have been to Las Vegas many times, but I am no expert.(and others might have more insight)
If this was my first trip there I would try to stay somewhere in the middle of The Strip. I would say that you staying at Caesar's would be about in the middle. Maybe Harrah's, Flamingo, or Bally's. I don't know what the rooms are like...just a place mid strip. I would try to have 3 full days to explore other casino's.

I would take a day and go to all of the casinos south of where you are staying (toward airport) the 2nd day I would use to explore all the casinos to the north.( An on the 3rd day go to Fremont st. That is where a majority of the older and smaller casinos are. I like the feel of the older places. The history. I also feel like I'm a little luckier in those small places. The mob museum, neon museum ect.

You might also consider looking into the bus schedule for the strip. I believe they have a bus called "The Duece" it is a hop on hop off type of deal. You buy day passes(I think.. Never done it) I know we rent a car every year we go(we have a timeshare off Harmon) and try to avoid driving on The Strip whenever possible. ( I'm talking about any points between MGM and Circus Circus.) North and South of that area is ok, but between those points you will be stuck in traffic most day and night.
Also ..... Plan on what casinos or other points of interest are most important to see. It is almost impossible to stay on a plan and trying to fit everything in. You just end up staying too long at one place looking at stuff or "getting lost" inside one of these huge casino complexes. And then you figure that the next casino is just next door, but it could take 30 minutes walking to get out of one and into the next.
Also....bring comfortable walking shoes. You can easily track 10+ miles walking in a day.
*** signing up at certain casinos might get you free slot/table play*** research which casino s offer those deals, but remember it will take a few minutes to sign up. Sometimes there is a line to do so.