New running shoes - where to buy?

If you don't know what the best shoe is for you then yes, they absolutely do.  I'm not familiar with Snail's Pace but my run shop has fit me, watched me run on the treadmill and now I run with their training group so they watch me run 3x per week for my workouts and can work with me if I'm having any issues.  My shop also offers a loyalty program so for every $250 I spend I get a $25 credit which adds up pretty quickly when talking about shoes, clothing and other gear I might buy from them.  They also offer short PT appointments every other week for free which is great if you have something going on that you want to get some thoughts on.  My shop is owned and operated by 2 former Olympians and they are able to pull in some awesome speakers as well. I've listened to Jeff Galloway, Steve Jones and Arturo Barrios speak so far.  As an added bonus because I know everyone who works there I can use the shop as a bathroom/water stop on long runs (and get a moment or two of encouragement if I need it too).

That being said, if you are just looking to buy shoes, don't care about the added benefits other than price and you know what shoe works for you then by all means go on price. 

runningwarehouse.com has some great deals, especially if you already know what shoe you want. I just bought a pair of Brooks Trance 8's for $50 - they retail for $140.

Look at a store to get an idea and to get measured - then shop online. This is easier with shoes - I considered it with a tri bike, but I ended up buying in a store.

Some people will tell you to not buy online, but I haven't had any problems.

What do you mean by off the rack at discounters? Are you describing shoes from a place like Walmart or Target? Those kind of "running" shoes are for people who might run a mile a week. The higher priced shoes at a running store are for people who are more serious about running and need a shoe with support and cushioning that will withstand the rigors of longer runs and higher volume. It's really no different than trying to be a serious bicyclist and using a Walmart bike.

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I buy most of my shoes there. They have free shipping both ways so you can order a whole bunch, try them on at home, and return the ones you don't like.

But if you've never worn real running shoes then I would definitely visit a specialty store first, get an expert fit, buy the first pair from them (with a return guarantee), and then go from there. The shoes might be a bit pricier than you expected but it's worth it. Nothing sucks more than running injuries that put you out of commission for weeks.

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There is no _best_ shoe.

Shoes are a very individual thing based on your foot shape, your natural pronation, your arch shape, your running style, etc. 

A good running store offers the extremely valuable service of helping you find the right shoe for you.  For me, that's certainly been worth an extra $20. 

Now, saying that, I took a look at Snail's Pace on Yelp, and the reviews seem to indicate that your experience very much depends on who's in the store at any given time.  It seems that some of the staff at that store are extremely knowledgable, others are useless. 

I would patronize a local running store. Not only do they offer proper fitting many are active
in the community, sponsoring races, clinic's  and the like.