Because of Lego's expansive world wide brand recognition and the fact that none of their competitors are really serious threats Lego prices vary very little from place to place. They also rarely go on sale and when they do the savings are usually quite minimal (I have collected Legos continuously for almost 3 decades and can count on one hand the number of times I have seen sets on sale at greater than 10% off in a retail store that was not going out of business). In light of that if your primary goal is speed and you don't mind paying full price you can walk into pretty much any store and purchase the set you want with assurance that another place in town won't be selling it cheaper.
I got very excited as a kid when the set pictured below was 3 dollars cheaper at a Wal-Mart we stopped at while on vacation (my hometown did not have one at that time).
My excitement over three dollars in savings was justified because a difference in regular price of even that paltry amount is rare between major retailers.
As Lego's product line has expanded the major retail stores (Wal-Mart, Target, etc.) have not greatly increased their shelf space. As a result they tend to carry only the "best sellers" so to speak. They will have most of the major sets, but will likely not carry all of the sets for a given theme so depending on what you are looking for they may not have it. They also usually do not have specialty sets like the Imperial Flagship which i had to order from Lego.com as it was the only place you could get it.
If you want the best for selection or are looking for something unique there are 3 places to go.
1. Lego.com: This one is obvious but it still needs to be stated. Every set available is on sale here. Around Christmas they usually run a sale where if you spend enough you don't pay shipping and they will run year round promotionals where they give away little sets.
2. Lego Retail Stores: These stores are factory direct from Lego and are basically their shop at home site in a retail setting. Same sets and same prices, the advantage of course is that you don't have to pay shipping. They also have monthly events which often involve give aways and have sale racks as well. These retail stores are now located in many major cities, check here to see where the one nearest to you is.
3. Toys R Us: Lego has some sort of special relationship with this national retailer and as a result they too have a fairly comprehensive selection. The advantage of Toys R Us is that there are a lot of them around and that you, again, don't have to pay shipping. They also run regular sales often buy one get one 50% off which can result in substantial savings. The disadvantage is that their prices are always about 10% higher than everywhere else so unless you are taking advantage of a sale this is probably your most expensive option.
While there is no silver bullet that will always allow you to avoid paying regular price for a set I have had some success with the following buying options.
1. Amazon.com: The online retail giant will often be a bit cheaper than everywhere else. And, as most sets are over $25 many orders will qualify for their free shipping. Their selection is roughly equivalent to the other large retailers, they will have the best sellers but not necessarily everything else.
2. eBay: When buying on eBay look for a buy it now option. Often sellers will take advantage of the sales I described at Toys R Us (buy one get one 50% off) and then sell the two sets at 80-90% of MSRP. Especially if they give free shipping this option can end up saving real money. Bidding on Lego sets on eBay, however, is something I would recommend that you avoid. Prices almost always go sky high above what you can walk down to Target and pick up the set for, this phenomena is something I don't understand. I got this harbor set from eBay $10.00 off MSRP with free shipping.
3. Bricklink.com: This site is the Lego collector's bread and butter. It is like eBay exclusively for Legos and minus any bidding. Any set, past or present, is available here. The advantage to this site in terms of new sets is that due to the competition you can usually find them a bit cheaper. These sellers do the same thing as the eBay sellers but often with slightly tighter margins due to all the competition which means slightly better savings. Furthermore if you are willing to get it slightly used or minus the minifigures you can realize even more savings. I picked up the castle below which retailed for $100 for a mere $20 because it was missing a few parts that I replaced with a subsequent $5 purchase.
One warning is that the online sellers are located all over the world so be careful to make sure the store you are buying from ships from your country or your shipping costs will be through the roof.
4. Craigslist: This options is the most hit or miss of all the options but it also has the greatest potential for savings. You can often find people who are moving or moms who are trying to clear out a kid's room and are offloading Legos, including new ones, cheap. Not something to depend on, but it is worth checking.
The Lego Chronicler