I recently dropped my iPhone 5S and the screen broke. It was still usable, but it really bothered me. So I went off to the Internet to find a local repair shop. While doing so I found that there are actually online stores that allow you to send in your phone and get it shipped back to you once it is repaired, without the hustle to actually go to a brick and mortar store. Bonus is most of those send in phone repairs shops are cheaper than the local vendors. You can even get a free diagnosis from most of the shops first, before committing to anything.
After some more research I found a really helpful portal called PhoneRepairCompare.com. They have a overview for virtual all current phone models (iPhone and Android, e.g. Samsung, HTC, Nokia, LG etc.) with price comparison and history of price development of multiple online phone repair shops.
Additionally they have a free database of local repair shops, in case you rather go straight to a store.
My phone is working again and I know what to do next time around. Any repair shop is free to sign up for their store and location.