Agree with previous post - massive co$$t difference between weekend and weekday.
Note that Sunday is usually considered a weekday. This may/not apply in December, depending on what time of the month you are going (e.g. if it's around New Years, then prices are sky-high, regardless of day of the week). However, there can be a good 'buzz' on Saturdays, given that it is so crowded, so maybe consider your average cost per night, and see does it come in within budget.
Better end of the Strip is the mid to south end (from Paris/Venetian/Bellagio, all the way down to the airport end near MGM Grand/NY NY/ Mandalay Bay).
The prices may be a bit more tempting on the mid-north end of the Strip (e.g. Stratosphere/ Riviera/ Circus Circus) but this is not the better end. You might also see good deals in the old dowtown area (near Binions etc.), but that area probably won't suit you the first time you go.
Have a great time - it's a fantastic place !!!