When buying a new LBS bike, what are some recommended accessories to purchase at the bike shop? Also, which accessories are you better off buying somewhere else due to price?

If you want to swap out tires, ask the LBS to pro-rate the new tires with the stock tires (nominal upgrade fee basically). Also check out lights, helmet, etc at LBS. Always better to try things out before buying. Other things such as pedals, cycling apparel, and shoes you can certainly purchase online. Really depends on what you are looking for.