How do I know where the best place to sell them is? (To get the best selling price)
As said before, you can sell them to vendors for 50% of the actual value. I believe if you sell them through your replicator (under the recycle option) it is 40%.
Honestly, I sell every item that I don't need through the replicator and I still have more than enough energy credits. The thing about this game is that there are many different currencies so energy credits aren't the most important and you don't need a whole lot of them.
Anyway back on topic, if you want to get the most money for your items sell them to vendors. You can also sell items through the exchange, but not all items will sell.
Originally Posted by CarlBooth
Is there a way I can tell where the vendors are in each sector?
All starbases (and some planets) have vendors. Here is an interactive map of earth space dock. You can use it to see where all the vendors are. On that page there is also links to the maps of other stations. No matter where you go you will only get 50%.
I saw someone say that the vendor at Defera Outpost 3 gives 60%. I'll check later when I get home.
Defera outpost 3 does buy at 60% face value, but it's currently bugged so that the only way to contact the outpost is by entering the combat instance (Daily "Aid the Deferi") and fighting off the Breen first.